1. Let ABC be a triangle and D be the mid-point of BC. Suppose the anglebisector of ∠ADC is tangent to the circumcircle of triangle ABD at D.Prove that ∠A = 90◦ also draw suitable diagrams.

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Saurabh Koranglekar · Answer

Vikas TU · Answer

Dear student Let DQ be the tangent to the circum-circle of Tr. ABD at D . /_ADQ=/_CDQ = x. Then by the Alternate Segment Theorem /_DBA=x and likewise /_BAD =x which makes DA = DB = DC since D is the midpoint of BC. In other words, D is the circum-centre of Tr. ABC and BC is its diameter. Then /_A = 90°.

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1. Let ABC be a triangle and D be the mid-point of BC. Suppose the anglebisector of ∠ADC is tangent to the circumcircle of triangle ABD at D.Prove that ∠A = 90◦ also draw suitable diagrams.

1. Let ABC be a triangle and D be the mid-point of BC. Suppose the anglebisector of ∠ADC is tangent to the circumcircle of triangle ABD at D.Prove that ∠A = 90◦ also draw suitable diagrams.

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1. Let ABC be a triangle and D be the mid-point of BC. Suppose the anglebisector of ∠ADC is tangent to the circumcircle of triangle ABD at D.Prove that ∠A = 90◦ also draw suitable diagrams.

1. Let ABC be a triangle and D be the mid-point of BC. Suppose the anglebisector of ∠ADC is tangent to the circumcircle of triangle ABD at D.Prove that ∠A = 90◦ also draw suitable diagrams.

2 Answers

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