Can you find the length X in the right triangle?

Hinzugefügt: 2026-06-04

[00:00:00]Can you find the length x?

[00:00:05]Suppose the center of the circle is O.

[00:00:13]And suppose this point is P.

[00:00:18]This point is Q.

[00:00:22]And this point is S.

[00:00:26]And we have AB is x.

[00:00:34]BC is 50.

[00:00:49]And now if we join OP and OQ then OP is radius. That will be five.

[00:01:06]And OQ is also radius.

[00:01:10]That will be five.

[00:01:13]And in any circle radius and tangent they are perpendicular on each other.

[00:01:27]That means OP it will be perpendicular on AB.

[00:01:36]And OQ it will be perpendicular on BC.

[00:01:44]So POQB it will be a square.

[00:01:57]And PO is five.

[00:02:01]OQ is five.

[00:02:04]That means BQ it will be also five.

[00:02:09]And BP it will be also five.

[00:02:16]And BC is 50.

[00:02:21]BQ is five.

[00:02:24]That means CQ will be 45.

[00:02:29]And AB is X.

[00:02:33]BP is five.

[00:02:37]So AP it will be X minus five.

[00:02:46]And Now in any circle from any point P if we make two tangent on the circle suppose this point is A and this point is B then PA and PB they will be equal.

[00:03:29]So from point A AP is X minus five.

[00:03:38]That means AS it will be also X minus five.

[00:03:45]And from point C CQ is 45.

[00:03:52]So, C is It will be also 45.

[00:04:00]And now AB is squared plus BC is squared It will be AC is squared.

[00:04:16]And AB is X is squared.

[00:04:19]BC is 50 is squared.

[00:04:24]And AC is X minus 5 plus 45.

[00:04:35]is squared And X is squared plus 50 is squared is X plus 40 is squared.

[00:04:51]And It is X is squared plus 2500 is X is squared plus 40 is squared is 1600 plus two times X times 40 is 80X.

[00:05:18]And X is squared will get cancelled.

[00:05:25]So, 2500 is 1600 plus 80X.

[00:05:34]And 2500 minus 1600 is 80X.

[00:05:47]And 900 is 80x.

[00:05:52]So, x will be 900 divided by 80.

[00:06:02]And zero will get cancelled.

[00:06:06]And two times 45 is 90.

[00:06:10]Two times four is eight.

[00:06:14]So, it is 45 divided by four.

[00:06:20]So, x is 45 divided by four.

[00:06:25]>> [music]