Question

What is length of chord of a circle with its radius as 5 cm and perpendicular distance from centre is 4 cm?

• A. 12 cm
• B. 10 cm
• C. 6 cm
• D. 3 cm

Answer 1

The correct option is C 6 cm

Radius of the circle, $OA=5$ cm
$OP=4$ cm
We know that, the perpendicular from the center of a circle to a chord bisects the chord.
∴ $AP=PB$
Consider triangle $OPA.$
By pythagoras theorem,
$A{P}^2$ = $5^2-4^2$
$A{P}^2$ = $3^2$
$AP$ = $3$ cm
$AP=PB=3$ cm
$AB=AP+PB$
∴$AB=6$ cm
Hence, the length of the chord is 6 cm.