Question

$HI$ and $JK$ are two parallel chords of a circle with centre $O$. They are opposite sides to the centre such that $HI=8$ cm, $JK=6$ cm and the distance between them is $7$ cm. Then, the radius of the circle is

• A. $10$ cm
• B. $4$ cm
• C. $5$ cm
• D. $3$ cm

Answer 1

The correct option is C $5$ cm

Consider the figure shown. Let $O$ be the center of the circle and $ON$ and $OM$ be the perpendicular bisectors of $JK$ and $HI$ respectively. (Perpendicular from center of circle to chord is also its bisector)

Hence, let $r$ be the radius of the circle and $x$ be the length of $ON$.

$\therefore$ in $△ONK$, applying the pythagorus theorem, $r^2=3^2+x^2$ ... (1)

Also, in $△OMI$, applying the pythagorus theorem, $r^2=4^2+(7-x{)}^2$ ... (2)

From (1) and (2), we get

$3^2+x^2=4^2+(7-x{)}^2⟹x=4$

Hence, substituting this in (1), $r=\sqrt{3^2+4^2}=5$

This is the required answer.