Question

a circle has radius root 2 cm. It is divided into 2 segments by a chord of length 2cm. proved that angle subtended by the chord at the point in measure segment is 45 degree

Answer 1

In ΔOQR
OQ² + OR² = QR²

(√2)² + (√2)² = QR²

2 + 2 = QR²
4 = QR²


In right angle ΔOQR
∠QOR = 90°

As the angle at the centre is double the angle on the remaining part of the circle, so
∠QOR = 2∠QPR
90° = 2∠QPR
∠QPR = 45°