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If C be a circle with centre O and radius 5 cm, then locus of mid-points of equal chords of C each of length 6 cm is a

A) concentric circle whose radius is 7 cm.
B) concentric circle whose radius is 4 cm.
C) straight line parallel to some chord of length of 6 cm.
D) straight line perpendicular to some chord of length of 6 cm.

Correct Answer:


B) concentric circle whose radius is 4 cm.

Description for Correct answer:

Let M (x, y) be the mid-point of any chord

AB = 6 cm of the given circle \( \Large x^{2}+y^{2}=25 \)

Clearly, OM is perpendicular to AB

From right angled triangle OMB

\( \Large OB^{2} = OM^{2}+MB^{2} \)

Therefore, \( \Large 5^{2}= \left(x-0\right)^{2}+ \left(y-0\right)^{2}+3^{2} \)

=> \( \Large 25 = x^{2}+y^{2}+9 \)

=> \( \Large x^{2}+y^{2} = 16 = 4^{2} \)

Hence, locus of mid-point is a concentric circle of radius 4 cm.

Part of solved Loci and concurrency questions and answers : >> Elementary Mathematics >> Loci and concurrency

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