Question

Question !!

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

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Answer 1

The distance of the chord from the centre is 6 cm

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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.