MathLabs

Problem 4

Let ABCD be a convex quadrilateral such that CD is tangent to the circle with diameter AB. Prove that AB is tangent to the circle with diameter CD if and only if BC∥ADBC\parallel AD.
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AB tangent⟺BC∥ADAB\text{ tangent}\Longleftrightarrow BC\parallel AD
Detailed analysis

Combining this intersecting-lines case with the parallel case proves the required equivalence.