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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.

jogesh , 7 Years ago
Grade 12
anser 2 Answers
Saurabh Koranglekar

Last Activity: 5 Years ago

576-2080_IMG_20200212_152939.jpg

Vikas TU

Last Activity: 5 Years ago

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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