Assertion Reasoning Quiz

Question 1 of 6

Assertion: If two towns are 18 km apart, the smallest circular ring road passing through both towns has radius 9 km and its centre is the midpoint of the segment joining the towns.
Reason: The centres of all circles passing through two given points lie on the perpendicular bisector of the segment joining those points.

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

Select one option. Answers are shown after the test.

Question 2 of 6

Assertion (A):
Any geometric parallelogram that is inscribed within a circle must definitively be a rectangle.
Reason (R):
The sum of two opposite angles of a cyclic quadrilateral is \(180^\circ\).

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.

Select one option. Answers are shown after the test.

Question 3 of 6

Assertion: The circumcentre of an obtuse-angled triangular signboard lies inside the signboard.
Reason: In an obtuse-angled triangle, the perpendicular bisectors of the sides intersect outside the triangle.

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.

Select one option. Answers are shown after the test.

Question 4 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.

Select one option. Answers are shown after the test.

Question 5 of 6

Assertion (A):
Two distinct chords \(PQ\) and \(RS\) in a circle of radius 8 cm both have a length of 8 cm. The angle subtended by chord \(PQ\) at the centre is exactly equal to the angle subtended by chord \(RS\) at the centre, and both are \(60^\circ\).
Reason (R):
Equal chords of a circle subtend equal angles at 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.

Select one option. Answers are shown after the test.

Question 6 of 6

Assertion (A):
In a cyclic quadrilateral \(ABCD\), if the side \(AB\) is extended to a point \(E\), then the exterior angle \(\angle CBE\) is equal to the interior opposite angle \(\angle ADC\).
Reason (R):
The sum of two opposite angles of a cyclic quadrilateral is \(180^\circ\).

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.

Select one option. Answers are shown after the test.

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