Let ABC be a triangle with circumcentre O. The points P and Q are interior pointsof the sides CA and AB, respectively. Let K, L and M be the midpoints of the segments BP, CQand PQ, respectively, and let I be the circle passing through K, L and M. Suppose that the linePQ is tangent to the circle I. Prove that OP = OQ.

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Let ABC be a triangle with circumcentre O. The po sides CA and AB, respectively. Let K, L and M be the mid 2, respectively, and let I be the circle passing through K, I tangent to the circle Prove that OP = 00

Let ABC be a triangle with circumcentre O. The po sides CA and AB, respectively. Let K, L and M be the mid 2, respectively, and let I be the circle passing through K, I tangent to the circle Prove that OP = 00

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter6: Circles

Section6.2: More Angle Measures In The Circle

Problem 48E: Given concentric circles with center O, ABC is inscribed in the larger circle, as shown. If BC is...

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Question

Let ABC be a triangle with circumcentre O. The points P and Q are interior points
of the sides CA and AB, respectively. Let K, L and M be the midpoints of the segments BP, CQ
and PQ, respectively, and let I be the circle passing through K, L and M. Suppose that the line
PQ is tangent to the circle I. Prove that OP = OQ.

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