Circle geometry -2 problems

kurdupel · #1 $Old$ December 2nd, 2008, 08:23 PM

And

I'm having problems figuring these two problems out. Thanks.

Soroban · #2 $Old$ December 3rd, 2008, 06:57 AM

Hello, kurdupel!

Theorem: If the opposite angles of a quadrilateral have a sum of 180°,
. . . . . . . the quadrilateral is cyclic.

The sum of the interior angles of any quadrilateral is 360°.

Angle B and C are right angles: . $\angle B + \angle C \:=\:180^o$

That leaves 180° for angles O and A: . $\angle O + \angle A \:=\:180^o$

Therefore, $ABOC$ is a cyclic quadrilateral.

Theorem: Tangents to a circle from an external point are equal.

Hence: the two tangents from A are both 10 units long,
. - . . . the two tangents from B are both 12 units long,
. - . . . . . . etc.

Got it?

kurdupel · #3 $Old$ December 3rd, 2008, 01:41 PM

Thanks a lot I appreciate it.