Question

What is the length of $AB$ ?

Answer 1

Each circle has radius $1.5$ units,$2$ units and $3$ units.

Let us construct a right angle triangle whose leg$=3-2=1$unit

$\Rightarrow$ hypotenuse$=2+3=5$units.

Other leg$=\sqrt{5^2-1^2}=\sqrt{24}=2\sqrt{6}$

Let us construct a right angle triangle at the center.

Join $DC\Rightarrow OA=EC=1.5$units.

Leg$=3+3-2-1.5=2.5$units.

$\therefore ED=2.5$units.

$\therefore$Hypotenuse$=1.5+2=3.5$units.

Other leg$=\sqrt{{3.5}^2-{2.5}^2}=\sqrt{6}$ units.

$\therefore AB=\sqrt{6}+2\sqrt{6}=3\sqrt{6}\approx 7.35$ units.