Question 9
A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is
Solution
Let the length of radius be 'r'.
From the above diagram,
$$x^2+r^2=6^2\ $$....(i)
$$\left(10-x\right)^2+r^2=8^2\ $$----(ii)
Subtracting (i) from (ii), we get:
x=3.6 => $$r^2=36-\left(3.6\right)^2$$ ==> $$r^2=36-\left(3.6\right)^2\ =23.04$$.
Area of circle = $$\pi\ r^2=23.04\pi\ $$
Area of rhombus= 1/2*d1*d2=1/2*12*16=96.
.'. Ratio of areas = 23.04$$\pi\ $$/96=$$\frac{6\pi}{25}$$
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