Question

PT is a diameter of the circle with centre O. Diameter PT is perpendicular to chord QR at point S. Then, $△$ PQR is an isosceles triangle.

• A. True
• B. False

Answer 1

The correct option is A True

We know that perpendicular from the centre of the circle to a chord bisects the chord. Hence QS = SR.
Now, in triangles $△$PQS and $△$PSR,
QS = SR
PS is the common side
$\angle$PSQ = $\angle$PSQ = 90${}^{\circ }$
Hence $△$PQS $\cong$ $△$PSR, using SAS congruency
$⟹$ PQ = PR [CPCT]
Hence $△$PQR is an isosceles triangle.
Therefore the given statement is true.