Mathematics
Assertion (A): In a circle, equal arcs suspend equal angles at the centre.
Reason (R): In the same circle, equal chords cuts off equal arc.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Answer
We know that,
Arcs of equal lengths subtends equal angles at the center of the circle.
∴ Assertion (A) is true.
We know that,
The chords of equal length cut off equal arcs.
∴ Reason (R) is true.
∴ Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Hence, option 4 is the correct option.
Related Questions
Consider the following two statements.
Statement 1: A line which meets a circle in two points is called a secant of the circle.
Statement 2: All radii of a circle are equal.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Assertion (A): Equal chords of a circle are equidistant from centre.
Reason (R): Chords of a circle that are equidistant from the centre of a circle are equal.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Assertion (A): In adjoining figure, AB is diameter of the circle with centre O.
If chord AC = chord AD, then we can conclude that ars BC = arc DB.
Reason (R): In adjoining figure, we can conclude that if chord AC = chord AD, then arc AC = arc AD.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
In the adjoining figure, a chord PQ of a circle with center O and radius 15 cm is bisected at M by a diameter AB. If OM = 9 cm, find the lengths of :
(i) PQ
(ii) AP
(iii) BP.
