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Mathematics

Assertion (A): Equal chords of a circle subtend equal angles at the centre of the circle.

Reason (R): One and only one circle can be drawn passing through three points.

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Circles

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Answer

Let AB and CD are two equal chords of a circle with center O.

Equal chords of a circle subtend equal angles at the centre of the circle. Chord Properties of a Circle, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

In Δ AOB and Δ COD,

OA = OC (Radii of a circle)

OB = OD (Radii of a circle)

AB = CD (Given)

By SSS congruency criterion,

Δ AOB ≅ Δ COD

Using corresponding parts of congruent triangles,

∠AOB = ∠COD

Assertion (A) is true.

Through three non-collinear points, exactly one circle can pass.

Through three collinear points, no circle can be drawn.

Reason (R) is false.

A is true, R is false.

Hence, option 1 is the correct option.

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