Listen NCERT Audio Books to boost your productivity and retention power by 2X.
If PT is a tangent to a circle with center O and PQ is a chord of the circle such that ∠QPT = 70°, then find the measure of ∠POQ.
Given: PT is a tangent to a circle with center O and PQ is a chord of the circle such that ∠QPT = 70°
To Find: ∠POQ = ?
Now,
∠OPT = 90°
[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]
∠OPQ + ∠QPT = 90°
∠OPQ + 70° = 90°
∠OPQ = 20°
Also,
OP = OQ [Radii of same circle]
∠OQP = ∠OPQ = 20°
[Angles opposite to equal sides are equal]
In △OPQ By Angle sum property of triangles,
∠OPQ + ∠OQP + ∠POQ = 180°
20° + 20° + ∠POQ = 180°
∠POQ = 140°