Can You Find the Radius of the Circle?

[00:00:00]Given AB is 8 and PQ is 6 and we have to find the radius of the circle.

[00:00:17]In any circle if PQ is a chord and O is the center and from O if we make a perpendicular on PQ then it will bisect the chord.

[00:00:44]And we have PQ is 6.

[00:00:50]That means PB it will be 3 and BQ it will be 3.

[00:01:02]And now if we join OP then AO and PO they are radius.

[00:01:22]Suppose X.

[00:01:25]AO is X and PO is X.

[00:01:32]And BO is AB AO and AB is 8 AO is X.

[00:01:46]BO is 8 - X.

[00:01:53]And >> Now, OP is squared.

[00:02:10]It will be PB is squared plus OB is squared.

[00:02:18]And OP is X is squared.

[00:02:22]PB is three is squared.

[00:02:25]Plus OB is 8 minus X is squared.

[00:02:33]And X is squared is nine plus 64 plus X is squared minus two times eight times X is 16 X.

[00:02:51]And X is squared will get cancelled.

[00:02:57]So, zero is 73 minus 16 X.

[00:03:04]So, 16 X is 73.

[00:03:09]That means X it is 73 divided by 16.

[00:03:21]>> [music]