Question

Two parallel chords on the same side of the centre of a circle are $10cm$ and $24cm$ long and their distance apart is $7cm$. Calculate the radius of the circle.

• A. $13cm$
• B. $8cm$
• C. $5cm$
• D. $7cm$

Answer 1

The correct option is A $13cm$

Let $PQ=10$ cm and $RS=24cm$ be the 2 chords. Lets take a perpendicular line $OA$ to both $PQ$and $RS$where B lies on $RS$and A on $PQ.$ Since $OA$ is perpendicular to the chords and passes through center, the chords are bisected by $OA$.

$⟹RB=SB=\frac{24}{2}=12cm$

$⟹PA=QA=\frac{10}{2}=5cm$

In $△OBS$

$O{B}^2=O{S}^2–S{B}^2$

$OB=\sqrt{r^2–{12}^2}$

Similarly In $△OAQ$

$OA=\sqrt{r^2–5^2}$

$OA–OB=7$

$+\sqrt{r^2–7^2}-\sqrt{r^2–{12}^2}=7$

$r=13$