Question

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11 the question

Answer 1

Answer:

Hope this helps.

There's a mistake in the problem.  It should say "prove that QR+PR=RO".

OR bisects the angle ∠PRQ, so ∠PRO = ∠QRO = 60°.

Since OP is a radius and PR is a tangent, ∠OPR = 90°.

Therefore ∠POR = 30°.

So triangle OPR is half an equilateral triangle with side OR.  Consequently, PR = OR/2.

Similarly, triangle OQR is half an equilateral triangle with side OR, so QR = OR/2.

It follows that

PR + QR = OR