Question

3. In the figure, O is the centre of the circle. A point Q is taken on the tangent PQ drawn to the circle at the point P, so that PQ = 4 cm and angle PQO = 45°, calculate the radius of the circle.​

Answer 1

OPR=90∘

∠OPQ+∠QPR=90∘

∠OPQ+50°=90∘

∠OPQ=∠OQP=40∘    (Since OP = OQ = radii; so Isosceles traingle OPQ)

Again,

∠POQ+∠OPQ+∠OQP=180∘    ( Angle sum property of triangle)

∠POQ+40∘+40∘=180∘

∠POQ=180∘–40∘–40∘

= 100°