Assertion Reasoning Quiz

Question 1 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 2 of 6

Assertion: Two observers standing at different points on the same arc of a circular track see the endpoints of a fixed chord under equal angles.
Reason: Each angle is half the same angle subtended by the chord at the centre.

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 3 of 6

Assertion (A):
Three points \(P, Q,\) and \(R\) lie on a straight straight line. It is possible to mathematically construct one, and exactly one, unique circle that passes through all three points simultaneously.
Reason (R):
There is a unique circle passing through three non-collinear points.

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 4 of 6

Assertion (A):
In a circle, a chord \(XY\) divides the circle. If it subtends an angle of \(45^\circ\) at a point \(P\) on the major arc, then it will strictly subtend an angle of \(135^\circ\) at any point \(Q\) situated on the minor arc.
Reason (R):
If a line segment joining two points subtends equal angles at two other points that lie on the same side of the segment, then the four points lie on a 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 5 of 6

Assertion: Every parallelogram can be inscribed in a circle.
Reason: A parallelogram that is cyclic must be a rectangle because its opposite angles are both equal and supplementary.

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 6 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.

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