Question

PRT is a tangent whose contact point is P to the radius OP of the circle. If POQ is 106° and QRT is 90°, find QPR and PQR

Answer 1

Step-by-step explanation:

As, In the figure,

OP = OQ ( radii of the same circle)

so, angle OQP = angle OQP ...... (1)

But, In ∆OPQ, by angle sum property

OPQ + POQ + QOP = 180°

OPQ + 106° + QOP = 180°

OPQ + OPQ = 180°-106° {By (1)}

2OPQ = 74°

OPQ = 37°

Now, It is given that, PRT is tangent to Circle,

hence OPR = 90°

and hence, QPR = 90°- 37°

QPR = 53°

In rt. ∆QRP, we have,

QRP = 90° and QPR = 53°

Hence, PQR = 180°- (90°+53°) = 180° - 143°

PQR= 37°.