Question

Please prove this question , tomorrow my maths pre board exam . I will mark as brainliest

Answer 1

here's your answer. All the best for your exams ! :-)

First you will do the construction and join OP & OQ.
Proof --> angle OPR = angle OQR = 90°[ Radius of the circle is perpendicular to the tangent to the circle at the point of contact]
We know that the centre lies on the bisector of the angle between two tangents
therefore angle PRO= angle QRO = 1/2 angle PRQ = 60°.
Now in ∆PRO,
cos 60° = PR/OR => 1/2 = PR/OR = 1/2OR = PR ----- (1)
Similarly in ∆QRO,
RQ = 1/2OR -------(2)
Adding (1) & (2) we get,
PR+RQ = 1/2OR+1/2OR
PR + RQ = OR.