In the adjoining figure, ABCD is a cyclic quadrilateral.
The line PQ is the tangent to the circle at A. If ∠CAQ: ∠CAP = 1: 2, AB bisects ∠CAQ, and AD bisects ∠CAP, then find the measure of the angles of the cyclic quadrilateral. Also, prove that BD is the diameter of the circle.
Solution:
More Solutions:
- The tangent at C meets AB produced at Q, ∠CAB = 34°.
- O is the center of the circumcircle of triangle XYZ.
- Two chords AB, CD of a circle intersect internally at a point P.
- PT is a tangent to the circle. Find TP if AT = 16 cm and AB = 12 cm.
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- Two chords AB, CD of a circle intersect externally.