Question

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

Solution

Given: AB and CD are two equal chords of congruent circles with centres O and O' respectively.
To Prove: ∠AOB = ∠CO'D.
Proof: In ∠OAB and ∠O'CD,
OA = O'C
| Radii of congruent circles
OB = O'D
| Radii of congruent circles

AB = CD    | Given
∴ ∆OAB ≅ ∆O'CD    | SSS Rule
∴ ∠AOB = ∠CO'D.    | C.P.C.T.

Some More Questions From Heron's Formula Chapter

for each arc, the remaining arc will have greater length.

Sector is the region between the chord and its corresponding arc.

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Heron's Formula

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

Some More Questions From Heron's Formula Chapter

for each arc, the remaining arc will have greater length.

Sector is the region between the chord and its corresponding arc.

A circle is a plane figure.

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

Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Prove that equal chords of a circle subtend equal angles at the centre.

In the adjoining figure is a circle with centre O. If ∠BAC = 60° and ∠DCB = 100°, then find ∠DBC.

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

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