Tangents and ANgles

Mel · #1 $Old$ May 17th, 2009, 08:49 PM

Tangents AX and Ay are drawn to circle P from an exterior point A. Radii PX and PY are drawn. If the measure of angle XPY = , find the measure of angle XAY.

earboth · #2 $Old$ May 18th, 2009, 01:49 PM

Quote:

Originally Posted by Mel $View Post$

Tangents AX and Ay are drawn to circle P from an exterior point A. Radii PX and PY are drawn. If the measure of angle XPY = , find the measure of angle XAY.

The complete figure is a kite composed of two right triangles. Therefore

$\angle(XAY)= 360^\circ-2 \cdot 90^\circ-\angle(XPY)$