Let ABC be a triangle and D be the midpoint of BC. Suppose the angle bisector of \(\angle ADC \) is tangent to the circumcircle of triangle ABD at D. Prove that \(\angle A = 90^o \) . (Regional Mathematics Olympiad, India, 2016)

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# Category Archives: geometry

## Orthogonality

Let ABC be a triangle and D be the midpoint of BC. Suppose the angle bisector of \(\angle ADC \) is tangent to the circumcircle of triangle ABD at D. Prove that \(\angle A = 90^o \) . (Regional Mathematics Olympiad, India, 2016)