Question

O is the centre of the circle and OM is perpendicular to chord PQ. If PQ= 6 cm and OM= 4 cm, then the radius of the circle is--​

Answer 1

Answer:-

Given:

▪︎O is the center of circle.

▪︎OM ( ⊥ to PQ ) = 4cm

▪︎PQ (chord) = 6cm

To Find:

▪︎Length of the radius

Construction:

Join OP

Solution:-

As we know,

Perpendicular from the the center of circle to the chord bisects the chord;

Hence,

MP = ½ of PQ

= MP = 6 ÷ 4

= MP = 3cm

In ∆ OPM

MP = 3cm

OM = 4cm

angle OMP = 90°

According to pythagorean triplet,

(MP)² + (OM)² = (OP)²

= 3² + 4² = OP²

= 9 + 16 = OP²

= OP = root over 25

= OP = 5cm

Hence, OP = radius = 5cm