Question

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) 11.5cm
b) 12cm
c) √69cm
d) 23c​

Answer 1

b) is correct 12 cm

Given

Radius of circle =13cm

length of chord =10cm

To Find

Distance of chord from its centre.

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

AB is a chord of length 10 cm

C is the midpoint of AB.

OB is the radius of length 13cm

AB = 10cm

AC = (1/2) ⋅ 10 = 5cm

OB = 5cm

In a right triangle OAC.

OC²= OA²- AC²

= √(13²- 5²)

= √(169-25)

= √144 cm

OC = 12cm

So, the distance of the chord from the centre is 12 cm

Answer 2

Question

Answer

$\bf \large given \: that \\ \bf radius \: = 13 \: cm \\ \bf chord \: = 10 \: cm$

______________________________

Since, the perpendicular from the centre of a circle to a chord bisects the chord.

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Now by using Pythagoras theorem

$\bf \large </p><p>(AO)^2 =(AL)^2 +(OL)^2 \\ \bf {(13)}^{2} = {(5)}^{2} + {(OL)}^{2} \\ \bf169 - 25 \: = (OL)^2 \\ \bf \sqrt{144} = (OL)$\\(OL) =12cm

So the distance of chord is 12cm