Question

Tangent to the circle with center o ,at the point A and B intersect at P,a circle is drawn with center P passing through A, prove that the tangent at A to circle with center P passes through o
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Answer 1

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