Question

In a circle of radius $5cm$, $AB$ and $AC$ are the two chords such that $AB=AC=6cm$. Find the length of the chord $BC$.

• A. $4.8cm$
• B. $10.8cm$
• C. $9.6cm$
• D. $Noneofthese$

Answer 1

The correct option is C $9.6cm$

$ABC$ forms a triangle with given circle as circumcircle

$⟹AB=AC=b=c=6cm,R=5cm$

$b=2R\sin B⟹\sin B=\frac{b}{2R}=\frac{6}{10}=\frac{3}{5}⟹\cos B=\frac{4}{5}$

$BC=a=2R\sin A=2\left(5\right)\sin (\pi -(B+C\left)\right)=10\sin 2B=20\sin B\cos B=20\times \frac{3}{5}\times \frac{4}{5}=9.6cm$