Question

Two concentric circles have a chord running through the outer one. The chord is the tangent of the inner circle and is $14$ cm. The outer circle is shaded and the inner circle is not. Find the exact area of the shaded region.

• A. $49\pi$
• B. $7\pi$
• C. $196\pi$
• D. none of these

Answer 1

Answer: (A)

$49\pi$

Let $AB$ be the chord

Lets draw a perpendicular line from $O$

$⟹OC\perp AB$

$AC=BC$

Given $AB=14cm$

$⟹AC=\frac{AB}{2}=7cm$

Consider $△AOC$

$O{A}^2=A{C}^2+C{O}^2$

$r_2^2=7^2+r_1^2$

$r_2^2–r_1^2=49$

Area of shaded region = Area of bigger circle – Area of smaller circle

$=\pi r_2^2–\pi r_1^2$

$=\pi \times 49=49\pi$