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Consider the ...

Question

Consider the following statements and choose the right option.

Statement 1: If two arcs are congruent, then their corresponding chords may not be equal.

Statement 2: If the angles subtended by two chords are equal, then the corresponding arcs are congruent.

A

Neither of the statements is true

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B

Only statement 1 is true

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C

Both the statements are true

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D

Only statement 2 is true

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Solution

The correct option is D Only statement 2 is true

Option B is the correct option.

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Similar questions

Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

If two chords of a circle are equal, then their corresponding arcs will be equal.

Q. From the following figure, choose the statements that are correct.
i) Congruent chords have congruent arcs.
ii) Congruent chords have equal central angles.
iii) Congruent arcs have congruent central angles.
iv) Chords equidistant from the center are congruent.

Q. If two chords of a circle are equal, then their corresponding arcs will be ______.

Q. Consider the following statements and choose the right option.

Statement 1: Two equal chords of a circle will not subtend equal angles at the centre if they are not parallel.

Statement 2: If two chords of a circle subtend equal angles at the centre, then the two chords are equal in length.

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