Question

Tangent at P to the circumcircle of triangle
PQR is drawn. If this tangent is parallel to
side, QR show that A PQR is isosceles.​

Answer 1

Answer:

DE is the tangent to the circle at P.

DE∣∣QR [Given]

∠EPR=∠PRQ  [Alternate angles are equal]

∠DPQ=∠PQR.....(i)  [Alternate angles are equal]

Let ∠DPQ=x and ∠EPR=y

Since the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment

∴∠DPQ=∠PRQ....(ii) [DE is tangent and PQ is chord]

From (i) and (ii)

∠PQR=∠PRQ

∴PQ=PR

Hence, △PQR is an isosceles triangle.