Thread: Circle geometry -2 problems
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Old December 3rd, 2008, 06:57 AM
Soroban Soroban is offline
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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?