Can you find the radius of the semicircle?

Added: 2026-05-24

[00:00:00]Can you find the radius of the semicircle?

[00:00:06]Suppose the center of the semicircle is O.

[00:00:16]And PQ is 28.

[00:00:27]And in any circle if PQ is a chord and O is the center and from the center O if we make a perpendicular on PQ suppose this point is M then it will be called PQ.

[00:01:08]So here from point O if we make a perpendicular on PQ suppose this point is M then PM and QM they will be PQ divided by two and PQ is 28 divided by two that will be 14.

[00:01:49]So PM is 14 and QM is 14.

[00:01:59]And Now in triangle OCM It is O C M This angle is 90° This angle is 45° So this angle It will be 90° - 45° That will be 45° And These two angles are equal That means OM and CM They will be also equal.

[00:03:18]And CM is 34 + 14 CM is 34 + 14 That is 48.

[00:03:31]So OM It will be also 48.

[00:03:39]OM is 48.

[00:03:46]And now If we join OP then OP is a radius.

[00:04:06]Suppose X.

[00:04:09]OP is X.

[00:04:13]And in triangle OPM OP is squared it will be OM is squared plus PM is squared.

[00:04:37]And OP is X is squared.

[00:04:44]OM is 48 is squared.

[00:04:48]Plus PM is 14 is squared.

[00:04:57]So X is squared is two is squared times 24 is squared plus two is squared times seven is squared.

[00:05:12]And X is squared is two is squared times 24 is squared plus seven is squared.

[00:05:24]And X is squared is two is squared times 576 plus 49.

[00:05:36]And X is squared is two is squared times 625.

[00:05:48]So X is squared is 2 is squared.

[00:05:54]And 625 is 25 is squared.

[00:06:01]So, x is squared is 2 * 25 is squared.

[00:06:09]And x is squared is 50 is squared.

[00:06:14]That means x it will be 50.

[00:06:22]And a radius it is x that will be 50.

[00:06:36]>> [music]