Find the length of a chord which is at a distance of 5cm from the center of a circle of radius 13cm .

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23cm

24cm

25cm

26cm

answer is B.

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Detailed Solution

Given,
There is a circle of radius 13cm .

https://www.vedantu.com/question-sets/aad77150-c3f1-47b1-9093-c11ddc60e6202176253955681544199.png

Let O be the centre of this circle. Such that OA=OB=13cm
Where AB is a chord of a circle. Which is at a distance of 5cm from the centre of the circle.
Such that OM=5cm
ΔOAM is a right angle triangle.
Therefore, applying Pythagoras theorem. We have
(OA)2=(OM)2+(AM)2
Substituting values in above we have
(13)2=(5)2+(AM)2
⇒169=25+(AM)2
⇒169−25=(AM)2
⇒144=(AM)2
⇒(AM)2=(12)2
⇒AM=12
Therefore from above we see that length of AM is 12cm
Hence, length of chord AB will be given as: 2×AM
Length of chord AB = 2×12
Length of chord AB = 24 cm .
Hence, the required length of the chord of a circle which is at a distance of 5 cm from the center is 24 cm.
So, the correct answer is “24 cm”.

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