Question

Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?

Answer 1

Answer:

Distance of chord from center = 6 cm

Step-by-step explanation:

Given,

Radius of circle = 10 cm

Length of chord of circle = 16 cm

Semi-length of chord = $\dfrac{16}{2}$

                                    = 8 cm

distance of chord from the center of the circle can be given as

$d\ =\ \sqrt{radius^2\ -\ (semi\ length\ of\ chord)^2}$

   $=\ \sqrt{10^2\ -\ 8^2}$

   $=\ \sqrt{36}$ cm

      = 6 cm

Hence, the distance of each chord from the center of circle is 6 cm.

Answer 2

Given :

Radius of Circle = 10cm

Length of Chord = 16cm

To Find :

Find the distance of these chords from the centre of the circle ?

Solution :

OR = OP = 10cm [Radius]

PQ = RS = 16cm [Chord]

Perpendicular drawn from the centre of the circle to the chord bisects the chord,

➣ PU = ½ × PQ

➣ PU = ½ × 16

➣ PU = 8cm

Applying Pythagoras Theorem in ∆OUP :

➣ (OP)² = (OU)² + (PU)²

➣ (10)² = (OU)² + (8)²

➣ 100 = (OU)² + 64

➣ 100 - 64 = (OU)²

➣ 36 = (OU)²

➣ √36 = OU

➣ 6cm = OU

Therefore,

Congruent chords of the circle are equidistant from the circle are :

➣ OU = OT = 6cm

Hence,

The distance of the chord from the centre is 6cm.