Question

Triangle PQR is inscribed in a circle with PR as a diameter. The perpendicular from P to the tangent at Q meets the tangent at S. Prove that PQ bisects angle SPR.

Answer 1

Answer on Question #46550 – Math - Geometry

Triangle PQR is inscribed in a circle with PR as a diameter. The perpendicular from P to the tangent at Q meets the tangent at S. Prove that PQ bisects angle SPR.

Solution.

$$PO = QO \ so \ < PQO = < QPR$$ $$< OQS = 90^0 \ so \ PS \ || \ OQ$$

Thus $< QPS = < PQO = < QPR$ and it proves that PQ bisects angle SPR.

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