Grade 11 MATHS ASSIGNMENT 2026 TERM 2 | EXPLAINED

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[00:00:01]All right, welcome back again learners.

[00:00:05]Um this video I'll be taking you through the assignment for Limpopo grade 11.

[00:00:11]Um without wasting time, let's go through the question together, then I explain to you. I'm going to take you through the the Euclidean geometry part, right?

[00:00:25]Okay, don't forget to subscribe so that you can access more of our videos.

[00:00:29]All right, let's start by analyzing the diagram.

[00:00:32]Um in the diagram below, O is the center of the bigger circle.

[00:00:37]That is O.

[00:00:38]Uh and the smaller circle passes through O.

[00:00:42]PAT is a common tangent to both circles at A.

[00:00:47]AC intersect the smaller circle at B. AO produced meets the bigger circle at D.

[00:00:53]DC and OB are drawn.

[00:00:56]All right, you can see that this is the tangent.

[00:01:00]Okay?

[00:01:01]So now let's go to the first question and then we see what is it that is requested of us. The first question is um prove that prove that OB is parallel to DC.

[00:01:16]All right, so for us to prove parallel lines, it's either we prove the F shape corresponding angles.

[00:01:25]Okay?

[00:01:26]So that we can prove the corresponding angles or you can also prove the what? The alternate angles. You can prove that or the co-interior.

[00:01:37]If you prove this, you have proved that the angles uh rather the lines are parallel, okay?

[00:01:45]So let's go straight to the question so that we can see if what we are doing it's correct or not.

[00:01:54]Okay.

[00:01:55]Now my first question as you can see, it is prove that OB is parallel to DC. Let's try to see which one can we prove.

[00:02:08]All right, OB I can see and the DC.

[00:02:12]All right, learner. Since this is a center, the line which pass through the center, it subtend angle at the circumference, which is 90.

[00:02:23]It's a diameter. So, which means that on the first question, 7.1, angle C is equal to 90° because AD is a diameter. So, you say angles in what?

[00:02:37]Semi second.

[00:02:42]Angles in semicircle.

[00:02:44]Right. So, if that one is 90°, you already got your two marks.

[00:02:50]So, let me try to check if I can prove that this one is also 90. Oh, it's easy.

[00:02:56]Right?

[00:02:58]It's easy. So, you're going to say What are you going to say? You're going to say angle B1 angle B1 is also 90°.

[00:03:12]Why are you going to say that? Because line drawn This is the first theorem. Line drawn from center.

[00:03:26]Line drawn from center to the chord.

[00:03:36]Line drawn from center to the chord.

[00:03:42]It's perpendicular to the chord. You see?

[00:03:45]Line drawn from center to the chord is perpendicular to the chord.

[00:03:51]I hope that one is clear.

[00:03:55]I hope that one is clear.

[00:03:58]Or or you can say angle A1 is equal to 90°.

[00:04:12]Angle A1 is equal to 90°. The reason is radius perpendicular to tangent. Radius perpendicular to tangent. You can prove it in this way, and then you can get it without any problem.

[00:04:31]Then, you can even say angle B1 is equal to angle A1 and is equal to 90°.

[00:04:44]tan chord theorem.

[00:04:49]You see, learners, so you've proved that tan chord theorem. I mean, if you want to show that this is 90. So, I was trying to show you that this one is 90, right?

[00:05:01]If you want to show that that one is 90, you can have it in other two methods.

[00:05:06]But, the most important thing I just wanted to show you that B1 is 90. But, this step is very important. You see this one?

[00:05:15]And then, we show that B1 is 90.

[00:05:18]This one or using this method. So, after we have proved, that's when now we can conclude and say DC or OB OB is parallel to DC.

[00:05:34]Then, you say corresponding angles are equal.

[00:05:40]Then, you're done. You're going to get your two marks there in this one and the one for the conclusion or on this or other one and the the reason, right?

[00:05:50]That is how to prove that OB is parallel to DC.

[00:05:56]Okay, learners, with what we have done, if this is 90 it means also B2 is 90. Let's go to the second one. So, this teach you the theorem. It means that these two are equal, okay?

[00:06:14]And these one are also what? Equal.

[00:06:17]Do you remember midpoint theorem?

[00:06:20]So, as for 7.2, this is what we're going to write, learners. You're just going to come here and say uh according to the midpoint theorem, you will say AO over AD AO over AD is equal to AB over A C.

[00:06:52]Now, AO over AD What is AB? Let's look at AB. It's twice. I mean, uh uh uh uh AC is twice AB. So, you this one will be AB and then this side is twice there. So, it will be over 2AB.

[00:07:12]So, the answer is 1/2.

[00:07:15]That is how you answer this question, learners. But, in your answers, don't forget to indicate that don't forget to indicate that DC is equal to 2 BO.

[00:07:29]Then, the reason you indicate mid point theorem. Then, you indicate the parallel lines.

[00:07:39]Right? That is how you answer the question seven of the assignment for grade 11.

[00:07:46]All right, let's go to the next question.

[00:07:51]Look at the diagram which is given there.

[00:07:54]AB Oh, in the in the figure AB is the diameter of the circle. CD is a tangent.

[00:08:03]Okay, we also have that.

[00:08:05]All right, let's go to the first question. Prove that A Let me put a dot.

[00:08:11]A ACED AC ED is a cyclic quad. How do you prove this?

[00:08:26]How do you prove that it's a cyclic quad, dear learners? It means that if you can show it's five marks. If you can show that A exterior angle of a cyclic quad they are equal.

[00:08:46]If you can show that the exterior angle of a cyclic quad are equal, then you have I mean the exterior angle of a cyclic quad is equal to interior angle. If you show that, it means you have proved it. ACED.

[00:09:03]All right, I'm going to prove this.

[00:09:06]Let me see, do I have a diameter? Yes, A. I have diameter A. So, my answer for 8.1, I will start by saying angle D3 because this is a diameter, this one.

[00:09:19]So, this one will be 90 for me. Angle D3 is equal to 90 degrees. I say angles in semi what?

[00:09:29]Angles in semicircle. I hope you get that.

[00:09:33]You get your beautiful two marks for the and reason.

[00:09:38]All right?

[00:09:41]As you can see, it means that if this one is 90 Uh, it means now we have proved it cuz already angle C1 Let's say angle C.

[00:09:58]Let's say angle C, the whole of angle C.

[00:10:01]So, angle C is equal to D3 angle D3 and is equal to 90°.

[00:10:19]Okay?

[00:10:21]So, with this information now you can simply go on that that that's a mark.

[00:10:26]You have proved that you have shown that.

[00:10:28]Now, the next thing will be therefore A C E D is a cyclic quadri lateral.

[00:10:46]Why?

[00:10:48]Converse.

[00:10:51]Exterior angle of a cyclic quad.

[00:11:01]That is the reason. You get your two marks for that.

[00:11:05]So, that is how you answer this question, learners.

[00:11:10]That is how you answer this question, the first one.

[00:11:14]It is talking about and it is also saying that CD is a tangent. Now, we have won on the first one. Okay? Let's go to the second one. A2 is equal to D1.

[00:11:31]8.2 A2 is equal to D1.

[00:11:37]Okay?

[00:11:40]Let's start by checking our D1.

[00:11:46]A2 A2 is equal to which angle?

[00:11:51]We started there.

[00:11:54]A2, you can see You can see A2 when you add it.

[00:12:05]Let's add this and see.

[00:12:08]Is A2 is equal to D1?

[00:12:11]All right. Let's use exterior and see.

[00:12:14]When we add these two this one this one it give you the one which is outside.

[00:12:22]Let's try that.

[00:12:24]Angle B plus angle A2 and angle A2 is equal to angle D1 plus angle D2 exterior angle of a triangle.

[00:12:49]All right.

[00:12:50]Now, with this information we can see something here.

[00:12:59]Uh but, let me say but.

[00:13:02]But, there are things you need to know.

[00:13:04]Angle B is this one.

[00:13:09]Look at B, learners.

[00:13:11]Is equal to this one.

[00:13:13]Angle B is equal to angle D2.

[00:13:19]Angle B >> Angle B is equal to angle what?

[00:13:34]Choose the correct pen.

[00:13:36]Angle D2.

[00:13:39]The reason here is tan chord theorem. You know this.

[00:13:45]This is what we are having.

[00:13:48]Right?

[00:13:51]Now, after doing that, it means where there is B, I'm going to put D2.

[00:13:55]So, it means this is this tells you that B and D2 will cancel. You'll be left with angle A2 is equal to angle D1. That is the answer for 8.2. Let's see if that is what we were required to prove. Let's see.

[00:14:16]Yes, A2 is equal to D1.

[00:14:21]All right, my learners. Let's try to go to the next one. Prove that is an isosceles triangle. Which one?

[00:14:28]Let's check.

[00:14:29]CDE. CDE is an isosceles triangle.

[00:14:36]Okay?

[00:14:39]CDE is an isosceles triangle.

[00:14:45]All right?

[00:14:47]Now, since we have proved CDE, that is 8.3.

[00:14:52]Triangle CDE.

[00:14:55]If I can prove that angle E is equal to If I can prove that this angle E is equal to angle D1, I've proved the isosceles.

[00:15:07]Let's try to check my RTP.

[00:15:09]Then, I'm going to say angle E I want to prove that is equal to angle D1.

[00:15:17]Let's see. What is it that is equal to to E? I'll start there.

[00:15:22]And then another angle which is equal to angle D1, I will start with the Angle D If you check, angle E is equal to A2.

[00:15:39]Then we say exterior angle of a cyclic quad.

[00:15:48]That is what we have done.

[00:15:50]Now D1 We have proved that is equal to A2.

[00:15:58]It's proven.

[00:16:03]It's proven, okay?

[00:16:05]So, let me bring my answers this side so that you can see what's happening.

[00:16:12]Okay? Now we have proved that angle E is equal to angle D1. That's my required to prove.

[00:16:20]Therefore, triangle Therefore, what does it mean? This means that side CE CE is equal to CD.

[00:16:39]Sides opposite equal what? Angles.

[00:16:44]Right? Therefore, triangle CDE is an isosceles triangle.

[00:16:57]It's an isosceles triangle.

[00:16:59]That's it, learners. Till we meet on the next video. I want you to do the Euclidean geometry part on this assignment. Don't forget to subscribe and like our videos and share to your friends. Till we meet on the next video. If you watch this and subscribe, then why not? We'll go to other questions.