Question

AB and CD are equal chords. If OE is 3 cm and AB is 8 cm, then the value of OC is .

• A. 4 cm
• B. 6 cm
• C. 5 cm
• D. 3 cm

Answer 1

The correct option is C 5 cm

In the given figure,Given: AB = CD = 8 cm and OE = 3 cm.
We know that, a line drawn through the centre bisects the chord and is perpendicular to it.
Thus, $CF=\frac{CD}{2}=4cm$
OE = OF = 3 cm ..... (Equal chords of a circle are equidistant from the centre.)
Consider $\Delta OFC,$
${OF}^2+{CF}^2={OC}^2$ .....(Pyhtagoras Theorem)
$3^2+4^2={OC}^2$
${OC}^2=9+16=25$
Thus, OC = 5 cm.