Listen NCERT Audio Books to boost your productivity and retention power by 2X.
In the given figure, O is the center of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70°, then ∠TPQ is equal to
In △OPQ
∠POQ = 70° [Given]
OP = OQ [radii of same circle]
∠OQP = ∠OPQ [Angles opposite to equal sides are equal]
By angle sum Property of triangle,
∠POQ + ∠OQP + ∠OPQ = 180°
70° + ∠OPQ + ∠OPQ = 180°
2 ∠OPQ = 110°
∠OPQ = 55°
Now,
∠OPT = 90°
[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]
∠OPQ + ∠TPQ = 90°
55° + ∠TPQ = 90°
∠TPQ = 35°