Question

Two circles with diameter $16cm$ and $8cm$ overlap $2cm$ as shown below in the figure. What is the sum of the lengths of the tangent chords $AB$ and $CD$ (Given $AB>CD$)

Answer 1

As AB and CD are tangents, both are perpendicular to OO'

In $\Delta$AOL, by Pythagoras theorem $A{L}^2=O{A}^2-O{L}^2-8^2-6^2$

$\Rightarrow AL=\sqrt{64-36}=\sqrt{28}=2\sqrt{7}$cm

Similarly on $\Delta$OCM, $C{M}^2=d{c}^2-O^{\prime }{M}^2=4^2-2^2$

$\Rightarrow CM=\sqrt{16-4}=2\sqrt{3}$cm

$\Rightarrow AB=4\sqrt{7}$cm, $CM=4\sqrt{3}$cm.