If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

The ratio of the radii of two circles is inversely proportional to the ratio of the angles subtended by arcs of the same length at the centre of the circles.

Step 1: Identify the given angles The angles given are 60° and 75°.

Step 2: Find the ratio of the angles The ratio of the angles is 60°/75° = 4/5.

Step 3: Find the ratio of the radii Since the ratio of the radii is inversely proportional to the ratio of the angles, the ratio of the radii is the reciprocal of the ratio of the angles. Therefore, the ratio of the radii is 5/4.