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State true or false.

The chords equidistant from the center of a circle are equal in length.

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True

False

answer is A.

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Detailed Solution

For the statement
1st we have drawn the circle of chords equidistant from the center.
Given,
The perpendicular line OM = ON
The cord = AB and CD
1st step, we have verified the chord
AB = CD
2nd step, joined the line OC and OA
Now, we have

OM ⊥ AB \hat{a} \frac{1}{2} AB = AM

ON ⊥ CD \hat{a} \frac{1}{2} CD = CN

Thus, we have considered the two triangles

△ AOM and △ CON

Radius of the circle

OA = OC

As per given,

OM = ON

∠ OMA = ∠ ONC = 90^{\circ}

Therefore, right hand side congruency we have

△ AOM ≅ ∠ CON

AM = CN \hat{a} \frac{1}{2} AB = \frac{1}{2} CD \hat{a} AB = CD

AB = CD

Hence The chords equidistant from the center of a circle are equal in length. this given statement is true.
Correct option is 1.

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