State true or false.

The equal chords of a circle are equidistant from the centre.

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True

False

answer is A.

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Detailed Solution

We have to check if the equal chords of a circle are equidistant from the centre.
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We know that corresponding parts of congruent triangles (CPCT) theorem states that if two or more triangles, which are congruent to each other, are taken then the corresponding angles and the sides of the triangles are also congruent to each other.
We know that AB=CD.
Since, the perpendicular drawn from the centre of a circle to bisect the chord,
So,

12 A B = 12 C D ⇒ B M = D N

Considering, ∆OMB and ∆OND,

∠ O M B = ∠ O N D = 900

…[Given]
OB=OD [Radii of the same circle]
BM=DN [Proved above]
Therefore, ∆OMB≅∆OND [By R.H.S.]
OM=ON [By C.P.C.T.]
Hence, the equal chords of a circle are equidistant from the centre and thus, the statement is true.
Therefore, option 1 is correct.

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