Question

a chord of length 24 cm is at a distance of 5 cm from the centre of the circle find the length of the chord of the same circle which is at a distance of 12 cm from the circle

Answer 1

here is your required solution

Answer 2

The length of the chord is 10 cm.

Step by step Explanation:

Given:

• A chord of length 24 cm is at a distance of 5 cm from the centre of the circle.

To find:

• Find the length of the chord of the same circle which is at a distance of 12 cm from the circle.

Solution:

Formula/Concept to be used:

• Find the radius of the circle.
• Apply Pythagoras theorem to find the half length of the chord.
• Twice the half length to find length of chord.

Step 1:

Find the radius of the circle.

See figure 1.

Perpendicular from centre bisects the chord AB.

Now, ∆OMB is right triangle, right angle at M.

OM= 5 cm

MB= 12 cm

Apply Pythagoras theorem to find OB(radius) of the circle.

${OB}^{2} = {OM}^{2} + {MB}^{2}$

or

${OB}^{2} = 25 + 144$

or

$OB = \sqrt{169}$

or

OB= 13 cm.

Thus, radius of circle is 13 cm.

Step 2:

Find the length of the chord.

See the attached figure 2.

Draw a chord CD, which is at 12 cm from the centre.

∆OED is right triangle, right angle at E.

OE= 12 cm

OD= 13 cm(radius)

Apply Pythagoras theorem,

${ED}^{2} = {OD}^{2} - {OE}^{2}$

or

${ED}^{2} = 169 - 144$

or

$ED= \sqrt{25}$

or

$\bf ED = 5 \: cm$

As, E is the mid-point of chord CD.

CD= 2ED

CD=10 cm

Thus,

Length of chord is 10 cm.

Learn more:

1) distance of a chord AB of a circle from the centre is 12cm and length of the chord AB is 10cm. find the diameter of the ...

https://brainly.in/question/6653415

2)in a circle of radius 13 cm is drawn at a distance of 12 CM of the centre find the length of the chord

https://brainly.in/question/6856048

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