Question

1. The radius of a circle is 13 cm and the length of one of its chords is 10 cm.
The distance of the chord from the centre is
(a) 11.5 cm (b) 12 cm (c) 169 cm (d) 23 cm
A chord is at a distance of 8 cm from the centre of a circle of
pls pls help me with explanation. don't post irreverent answer.​

Answer 1

✬ Distance = 12 cm ✬

Step-by-step explanation:

Given:

• Meaure of radius of circle is 13 cm.
• Length of chord of circle is 10 cm.

To Find:

• What is the distance of chord from centre of circle?

Construction: From O , draw OL perpendicular to AB.

Solution: Now in the circle .

• OA is radius of 13 cm.
• AB is chord with centre O such that AB = 10 cm.

As we know that perpendicular from the centre of a circle to a chord bisects the chord. Therefore,

➯ AL = 1/2(AB)

➯ AL = 1/2(10)

➯ AL = 5 cm

Now, in right angled triangle OLA , we have

• OL = Perpendicular
• AL = Base = 5 cm
• AO = Hypotenuse = 13 cm
• ∠OLA = 90°

Applying Pythagoras Theorem here

★ H² = B² + P² ★

$\implies{\rm }$ AO² = AL² + OL²

$\implies{\rm }$ 13² = 5² + OL²

$\implies{\rm }$ 169 = 25 + OL²

$\implies{\rm }$ 169 – 25 = OL²

$\implies{\rm }$ 144 = OL²

$\implies{\rm }$ √144 = OL

$\implies{\rm }$ √12 $\times$ 12 = OL

$\implies{\rm }$ 12 = OL

Hence, the distance of chord from the centre of circle is 12 cm. Option (b) is correct.

Answer 2

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