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Equal chords of a circle subtend equal a...

Equal chords of a circle subtend equal angles at the centre.

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To prove that equal chords of a circle subtend equal angles at the center, we can follow these steps: ### Step-by-Step Solution: 1. **Given Information**: - Let the two chords be \( AB \) and \( CD \). - Let the center of the circle be \( O \). - We know that \( \angle AOB = \angle COD \). ...
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Theorem:-1If two arcs of a circle are congruent; the corresponding chord are equal and Equal chords of a circle substends equal angles at the centre.

prove that the line joining the mid-point of two equal chords of a circle subtends equal angles with the chord.

Knowledge Check

  • r : Two chords of a circle subtend equal angles at centre if and only if they are equal. Statement r can be interpreted as

    A
    Two chords of a circle subtend equal angle at the centre if they are equal
    B
    Two chords of a circle are equal if they subtend equal angle at the centre
    C
    Both (1) & (2)
    D
    None of these

  • What is the length of the chord of a unit circle which subtends an angle at the centre ?

    A
    `sin(theta/2)`
    B
    `cos((theta)/(2))`
    C
    `2sin((theta)/(2))`
    D
    `2cos((theta)/(2))`

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    Recall that two circles are congruent if they have the same radil.Prove that equal chords of congruent circles subtend equal angles at their centres.

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