Question

Practice set 6.2
1.
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 ?
re at a distance of 5 cm from the centre.​

Answer 1

Correct 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?

Given :

• Radius of Circle = 10cm
• Length of each Chord = 16cm

To Find :

• The Distance of these chords from the centre of the Circle.

Solution :

✰ Let AB and CD be two chords and let OE be the perpendicular drawn from the centre of the circle to the chord AB. We know that, perpendicular drawn from the centre of the circle to the chord bisects the chord. So AE = EB = 8cm.

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✰ Now we will apply Pythagoras Theorem in the ∆AEO .

Using Pythagoras theorem :

⟼ (AO)² = (EO)² + (AE)²

⟼ (10)² = (EO)² + (8)²

⟼ 100 = (EO)² + 64

⟼ 100 - 64 = (EO)²

⟼ 36 = (EO)²

⟼ √36 = EO

⟼ 6cm = EO

✰ We know that congruent chords of a circle are equidistant from the circle. So, EO = OF = 6cm

⟹ Distance of these chords from the centre in 6 + 6 = 12cm

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