Two circles intersect each other at A and B. One of them passes through the center O of the other. AT is a tangent at A to the circle which passes through O. Prove that AO bisects angleBAT.

Asked by rushabhjain.avv | 30th Jan, 2019, 08:15: PM

Expert Answer:

O'A=O'O.....radii of the same circle

So, we have angle O'AO =O'OA=x......isosceles triangle theorem

now tangent perpendicular to the radius

angle O'AT=90

so angle OAT = 90 - x..........(1)

OO' will be perpendicular to AB, since O is equidistant from A and B, OA = OB radii of the same circle

so in that triangle

angle OAB= 90 - x............(2)

from (1) and (2)

angle OAT = angle OAB

Answered by Arun | 1st Feb, 2019, 11:18: AM