Assertion Reasoning Quiz

Question 1 of 6

Assertion (A):
Two intersecting chords \(AB\) and \(CD\) inside a circle are both recorded at a perpendicular distance of exactly 4 cm from the centre. Given this, if \(AB\) is 10 cm long, then \(CD\) must also be 10 cm long.
Reason (R):
Chords of a circle having the same length are all at the same distance from the centre of the circle.

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is not the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

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Question 2 of 6

Assertion (A):
When two separate circles intersect at two distinct points \(A\) and \(B\), the straight line connecting their centres serves as the exact perpendicular bisector of the common chord \(AB\).
Reason (R):
The line joining the centre of a circle and the midpoint of a chord of the circle is perpendicular to the chord.

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is not the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

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Question 3 of 6

Assertion: The angle formed at any point on a semicircular arch by joining that point to the two endpoints of the diameter is 90°.
Reason: A diameter subtends an angle of 90° at the centre of the circle.

A Both statements are true, and the second statement correctly explains the first. B Both statements are true, but the second statement does not correctly explain the first. C The first statement is true, but the second statement is false. D The first statement is false, but the second statement is true.

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Question 4 of 6

Assertion: A circular wheel without spokes or markings looks unchanged after a rotation of 137° about its centre.
Reason: Every diameter of a circle is a line of reflection symmetry.

A Both statements are true, and the second statement correctly explains the first. B Both statements are true, but the second statement does not correctly explain the first. C The first statement is true, but the second statement is false. D The first statement is false, but the second statement is true.

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Question 5 of 6

Assertion (A):
A triangular plot with side lengths 6 m, 8 m, and 10 m has a unique circumcircle. The circumcentre of this plot lies exactly at the midpoint of the 10 m boundary.
Reason (R):
For a right-angled triangle, the circumcentre lies at the midpoint of the hypotenuse.

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is not the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

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Question 6 of 6

Assertion (A):
If a triangle is inscribed within a circle such that one of its sides passes directly through the centre of the circle, it must be a right-angled triangle.
Reason (R):
The angle subtended by an arc at the centre of the circle is double the angle subtended by the arc at any point on the circle outside the arc.

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is not the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

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Assertion Reasoning Quiz