Question

Ajay traveled along a path which was straight up to 10 m (from point P to point T) and then went along an arc of a circle (from point T to point B) to reach his destination (B). Path PT is tangent to the circle at point T. If Ajay had travelled along the straight line joining his starting point P and his destination point B, he would have traveled 20 m and would have passed through the centre of the circle to which the arc belongs. The radius of the circle is(to which arc TB belongs) ___ m.

Answer 1

Let r be the radius of the circle of which the arc is a part.

$\because$ PT${}^2$= PA × PB

$\therefore$ 100 = (20 - 2r) × 20

$\therefore$ 40r = 400 − 100

$\therefore$ r = 7.5 m