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Q.

Let A, B be the centers of two circles of equal radii; draw them so that each one of them passes through the center of the other. Let them intersect at C and D. $\underset{̲}{AB}$ and $\underset{̲}{CD}$ are ____.

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Detailed Solution

Given that two circles have equal radii.
Draw two circles of equal radii taking A and B as their center such that one of them passes through the center of the other. They intersect at C and D. Join AB and CD.
In triangles AEC and BEC, Question Image

Question Image

⇒ AC = CB (Radius are equal)
⇒ CE = CE (Common in both triangles)
⇒ AE = EB (By construction)
By SSS, AEC is congruent to BEC
⇒∠ AEC = ∠ BEC = 90° (By CPCT)
So,

\underset{̲}{AB}

and

\underset{̲}{CD}

are at right angles.

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