Geometry Problem -1

Geometry Level 3

Equilateral A B C \triangle ABC is inscribed in a circle. A point P P lies on the circumference of the circle such that A P AP and B C BC intersect at point D D . Given that B P = 5 BP=5 and P C = 20 PC=20 , find A D AD .


The answer is 21.

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1 solution

Ajit Athle
Apr 25, 2018

By Ptolemy, AB,PC + AC.PB = AP.BC or AP = PB + PC = 25. Now we claim by similar triangles that 1/DP = 1/PB + 1/PC and therefore, 1/DP = 1/5 + 1/20 or DP = 4. Hence, AD = 25 - 4 = 21.

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