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: .

That leaves 180° for angles O and A: .

Therefore, 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?