And
I'm having problems figuring these two problems out. Thanks.
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: .$\displaystyle \angle B + \angle C \:=\:180^o$
That leaves 180° for angles O and A: .$\displaystyle \angle O + \angle A \:=\:180^o$
Therefore, $\displaystyle ABOC$ 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?