Question

A circle has two equal chords $AB$ and $AC$. Chord $AD$ cuts $BC$ in $P$. If $AC$ $=$ $12$ cm. and $AP$ $=$ $8$ cm, then the length of $AD$ in centimetres is

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

Answer 1

The correct option is D $18$

${12}^2-x^2=A{M}^2=8^2-y^2$
$\therefore {12}^2-8^2=x^2-y^2$
$=(x+y)(x-y)=x^2-y^2$
$=(x+y)(x-y)=BP.PC$
$\therefore AP.PD=80or8\times PD=80$
$\therefore PD=10andAD=18$