Let
be the tangent to the circle at
And,
[Given]
[Alternate angles are equal]
[Alternate angles are equal] ….. (i)
Let
As the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment, we have
[DE is tangent and PQ is chord]
So, from (i) and (ii),
Therefore, triangle
is an isosceles triangle.