A Very Nice Geometry Challenge

Ajouté : 2026-05-09

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

[00:00:05]If we complete the circle and extend PC and QD Suppose this point is M and this point is N and join MN then if ABCD is inside a circle then sum of opposite angles angle A plus angle C it will be 180° and also angle B plus angle D it will be 180° and here angle P is 90° that means angle N it will be also 90° and angle Q is 90° that means angle M it will be also 90°.

[00:02:05]And now we can see that the figure is symmetric about the diameter AB and CP is X.

[00:02:51]So DN it will be also X.

[00:02:58]And QD is 8.

[00:03:01]So MC it will be also 8.

[00:03:07]And SC is 6.

[00:03:11]So BD it will be also 6.

[00:03:17]And now in any circle if two chord AB and CD intersect at O then AO * BO it is CO * DO.

[00:03:45]And here AB and PM is intersecting at C.

[00:03:56]So, AC * BC it will be PC * MC.

[00:04:07]And AC 6 * BC is 26 + 6.

[00:04:16]BC is 26 + 6.

[00:04:20]And PC is X * MC is 8.

[00:04:26]And 6 * 32 is X * 8.

[00:04:35]And 8 * 4 is 32.

[00:04:43]So, 6 * 4 is X.

[00:04:47]And 24 is X.

[00:04:51]So, X is 24.

[00:04:59]>> [music]