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Triangles on the Same Base and between the Same Parallels

Assertion: If...

Question

Assertion: If two circles intersect at two points, then the line joining their centres is perpendicular to the common chord.
Reason: The perpendicular bisectors of two chords of a circle intersect at its centre.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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Solution

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Clearly, Assertion (A) and Reason (R) are both correct and Reason (R) is the correct explanation of Assertion (A).

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Similar questions

Q. Assertion: The radius of a circle is 10 cm and the length of one of its chords is 16 cm. Then, the distance of the chord from the centre is 6 cm.
Reason: The perpendicular from the centre of a circle to a chord (other than the diameter) bisects the chord.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. Assertion: A cyclic parallelogram is a square.
Reason: Diameter is the largest chord in a circle.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. Assertion: In a circles of radius 13 cm, there is a chord of length 10 cm at a distance of 12 cm from the centre of the circle.
Reason: A unique circle can be drawn to pass through three give non-collinear points.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. (i)
Assertion: A circle is not a rectilinear figure.
Reason: A figure formed by straight lines only is called a rectilinear figure.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.
(ii)
Assertion: All right angles are equal to one another.
Reason: A unique line passes through a single point.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. Assertion: Ray

\underset{A B}{\to}

has one end-point A.
Reason: Line segment

A B

has two end-points A and B.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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