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Part of 2019 OMMock - Mexico National Olympiad Mock Exam

Problems(1)

Similarity with centers of two circles

Source: Mexico National Olympiad Mock Exam 2019 P1

10/15/2019
Let C1C_1 and C2C_2 be two circles with centers O1O_1 and O2O_2, respectively, intersecting at AA and BB. Let l1l_1 be the line tangent to C1C_1 passing trough AA, and l2l_2 the line tangent to C2C_2 passing through BB. Suppose that l1l_1 and l2l_2 intersect at PP and l1l_1 intersects C2C_2 again at QQ. Show that PO1BPO_1B and PO2QPO_2Q are similar triangles.
Proposed by Pablo Valeriano
similarityCentergeometry