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Challenges on Equal Chords and their Distance from Centre

Find the rati...

Question

Find the ratio of the distance from the center of the circle to congruent sides of the triangles, if $△ A E C ≅ △ D F B .$

A

1 : 1

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B

2 : 1

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Solution

The correct option is A $1 : 1$
Given: $△ A E C ≅ △ D F B$
Let G is centre of the circle here.

$∴$ Vertex F corresponds to E and vertex B corresponds to C.
Congruent triangles have corresponding sides equal in length.

Hence, $F B = E C, A E = D F, A C = D B$ .
Chords of equal length are equidistant from the center of the circle.

$∴$ The required ratio is $1 : 1.$

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