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Question

$$AB$$ is diameter of a circle, $$CD$$ is a chord equal to the radius of the circle . Find the area of $$ABCD$$ if radius is $$\sqrt3cm$$ 


Solution

Radius of circle $$\sqrt3cm$$
Length of chord is given as $$2\sqrt{r^2-d^2}=r\\\sqrt{3-d^2}=\dfrac{r}{2}\\3-d^2=\dfrac{3}{4}\\d=\dfrac32$$
So the area of $$ABCD$$ is given as $$ r\times 2r\times d\\\sqrt3\times \sqrt3\times \dfrac32\\\dfrac92$$

Mathematics

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