HardMathematicsHigh School (9–10)Mensuration › Areas and PerimetersNumericalreasoningBoard Exam SAT

figure: ar-a1-chord.png Two circles have the same centre…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Two circles with the same centre O. The ring between the outer blue circle and the inner red circle is shaded orange. A green chord AB of the outer circle runs across the picture above the centre and touches the inner circle at its middle point M. A right angle is marked at M. The red radius OM of the inner circle is labelled r. The blue radius OA of the outer circle is labelled R. The part MA of the chord is labelled half chord.

Two circles have the same centre. A chord of the outer circle is $42\ \text{cm}$ long and touches the inner circle, which has a radius of $20\ \text{cm}$ . Find the radius of the outer circle and the area of the ring between the circles. Take $\pi = \dfrac{22}{7}$ .

Need a reminder? The key ideaShow

A ring has area $\pi(R^2 - r^2)$ . If a chord of the big circle touches the small circle, the area of the ring is $\pi \times (\text{half the chord})^2$ . A path outside a circle adds its width to the radius.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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