Question

A circle has two equal chords $AB$ and $AC$. Chord $AD$ cuts $BC$ in $E$. If $AC=12$ cm. and $AE=8$ cm, then $AD$ (in cm) is equal to

• A. $27$
• B. $24$
• C. $21$
• D. $18$

Answer 1

The correct option is D $18$

In $\Delta$ACD and $\Delta$ACE.
$\angle D=\angle B$...(angle in the same segment)
$\angle B=\angle C$...(angle opposite to equal sides)
$\therefore \angle D=\angle C$
$\angle$ A is common.
$\therefore$ from AA similarity $\Delta$ACD and $\Delta$ACE are similar.
$\therefore \frac{AC}{AE}=\frac{AD}{AC}$
or $\frac{12}{8}=\frac{AD}{12}$
or $8AD=12\times 12$
or $AD=\frac{12\times 12}{8}=18cm$