Question

The length of the cord of a circle is 16 cm and distance of cord from centerof the circle is 6 cm then findthe radius of circle.

Answer 1

Let AB is the cord.

Join O with A and B.

In ∆ OBM and ∆ OAM,

i) Angle OMB = Angle OMA ( right angles)

ii) OB = OA ( radii)

iii) OM = OM ( common side)

So, ∆ OBM ≅ ∆ OAM (by RHS)

By CPCT,

i) AM = BM

ii) AM = 8 cm

iii) OM = 6 cm

According to Pythagoras theorem,

OA=√(OM^2+AM^2) cm

=√(6^2+8^2) cm

=√ 36+64 cm

=√ 100 cm

= 10 cm

Hence, the radius of circle is 10 cm.