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 centres of the circles.

Let's denote the radii of the two circles as r1 and r2, and the angles subtended at the centres as θ1 and θ2.

According to the problem, θ1 = 120º and θ2 = 75º.

The ratio of the radii r1/r2 is equal to the inverse ratio of the angles θ2/θ1.

So, r1/r2 = θ2/θ1 = 75º/120º = 5/8.

Therefore, the ratio of the radii of the two circles is 5:8.

Question

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 centres of the circles.

Let's denote the radii of the two circles as r1 and r2, and the angles subtended at the centres as θ1 and θ2.

According to the problem, θ1 = 120º and θ2 = 75º.

The ratio of the radii r1/r2 is equal to the inverse ratio of the angles θ2/θ1.

So, r1/r2 = θ2/θ1 = 75º/120º = 5/8.

Therefore, the ratio of the radii of the two circles is 5:8.

Knowee AI · Accepted Answer

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 centres of the circles.

Let's denote the radii of the two circles as r1 and r2, and the angles subtended at the centres as θ1 and θ2.

According to the problem, θ1 = 120º and θ2 = 75º.

The ratio of the radii r1/r2 is equal to the inverse ratio of the angles θ2/θ1.

So, r1/r2 = θ2/θ1 = 75º/120º = 5/8.

Therefore, the ratio of the radii of the two circles is 5:8.

If the arcs of same length in two circles subtend angles of 120º and 75º at their centres. Find the ratio of their radii.

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