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Heron's Formula

Question

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

Solution

Each pair has at the most two common points.
(i)

No point common
(ii)

One point common
(iii)

Two points common
The maximum number of common points is two.

Some More Questions From Heron's Formula Chapter

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.

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.

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