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

figure: ar-a3-inscribed.png An equilateral triangle has all three corners on a circle of radius 12…

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

Two circles side by side, both with radius r and centre O. In the left circle, a red square has its four corners on the circle, and the four curved parts between the circle and the square are shaded orange. In the right circle, a red equilateral triangle has its three corners on the circle, and the three curved parts between the circle and the triangle are shaded orange. The captions are square and equilateral triangle.

An equilateral triangle has all three corners on a circle of radius $12\ \text{cm}$ . Find the area of the part of the circle that is outside the triangle. Take $\pi = 3.14$ and $\sqrt{3} = 1.73$ . Also write the exact form.

Need a reminder? The key ideaShow

A square with all corners on a circle of radius $r$ has the area $2r^2$ . An equilateral triangle with all corners on the circle has the side $r\sqrt{3}$ and the area $\dfrac{3\sqrt{3}}{4}r^2$ . The leaf of two quarter circles of radius $a$ in a square of side $a$ is $\left(\dfrac{\pi}{2} - 1\right)a^2$ .

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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