Question

Pq is the tangent at point c of the circle with centre o. If ab is a diameter and angle cab is 60 degree, find angle pca.

Answer 1

Answer:

Given : PQ is a tangent. AB is the diameter, ∠CAB = 30°

∠PAC = ?

In ΔAOC,

As, AO = CO      (Given)

so,  ∠CAO =  ∠OCA        (Angle opposite to equal sides are equal)

or  ∠CAB =  ∠OCA

but  ∠CAB = 30°

so,  ∠OCA = 30° .......................(1)

Since, OC ⊥ PQ    (Tangent is perpendicular to the radius at a point of contact)

==>  ∠PCO = 90°

==>  ∠OCA + ∠PCA = 90°

==>  30° +  ∠PCA = 90°

==>  ∠PCA = 90° - 30°

==>  ∠PCA = 60°

Thanks......................