Question

In the given figure, PQ R is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°. Find ∠PCA.

Answer 1

Given

• PQ is a tangent at point C.
• Center of circle = O
• Diameter = AB
• ∠CAB = 30°
• ∠ACB = 90° [Angle in the semi-circle]

To Find

• Find = ∠PCA

Solution

✏ In ∆ABC,

∵ Sum of interior angles of triangle is 180°...

∠CAB + ∠ACB + ∠CBA = 180°

30 + 90° + ∠CBA = 180°

∠CBA = 180° – 30° – 90° = 60°

∠PCA = ∠CBA…..[∵Angle in the alternate segment]

$\large \implies \boxed {\boxed {\tt \blue { \angle PCA = 60}}}$

Answer 2

Correct answer= In Fig. 8.14, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and. ∠CAB = 30o, find ∠PCA.

Answer is given in above pic⤴️