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Heron's Formula

Question

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Prove that a cyclic parallelogram is a rectangle.

Solution

Given: ABCD is a cyclic parallelogram.
To Prove: ABCD is a rectangle.

Proof: ∵ ABCD is a cyclic quadrilateral
∴ ∠1 + ∠2 = 180° ...(1)
| ∵ Opposite angles of a cyclic quadrilateral are supplementary
∴ ABCD is a parallelogram
∴ ∠1 = ∠2 ...(2)
| Opp. angles of a || gm
From (1) and (2),
∠1 = ∠2 = 90°
∴ || gm ABCD is a rectangle.

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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