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7.4

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 7.4 common tangent parallel to line

Source:

6/7/2020
Let ABCDABCD be a quadrilateral inscribed in the circle (O)(O). Let (K)(K) be an arbitrary circle passing through B,CB,C. Circle (O1)(O_1) tangent to AB,ACAB,AC and is internally tangent to (K)(K). Circle (O2)(O_2) touches DB,DCDB,DC and is internally tangent to (K)(K). Prove that one of the two external common tangents of (O1)(O_1) and (O2)(O_2) is parallel to ADAD.
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Tangentsparallelcyclic quadrilateraltangent circlesgeometry