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Heron's Formula

Question

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

Solution

Given: ∠AOB and ∠CO'D are the two equal angles subtended by the chords AB and CD of two congruent circles with centres O and O' respectively. (See Example 1)
To Prove: AB = CD.
Proof: In ∆OAB and ∆O'CD,
OA = O'C
| Radii of congruent circles
OB = O'D
| Radii of congruent circles
∠AOB = ∠CO'D    | Given
∴ ∆OAB ≅ ∆O'CD    | SAS Rule
∴ AB = CD.    | C.P.C.T.

Some More Questions From Heron's Formula Chapter

The centre of a circle lies in ________ of the circle. (exterior/interior).

A point, whose distance from the centre of a circle is greater than its radius lies in ________ of the circle. (exterior/interior).

The longest chord of a circle is a ________ of the circle.

An arc is a ________ when its ends are the ends of a diameter.

Segment of a circle is the region between an arc and ________ of the circle.

A circle divides the plane, on which it lies, in ________ parts.

(i) Line segment joining the centre to any point on the circle is a radius of the circle.

A circle has only finite number of equal chords.

If a circle is divided into three equal arcs, each is a major arc.

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

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