Mathematics
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).
Circles
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Answer
Given,
AB is the diameter of the circle with center O and, Chord AC = Chord AD.
We know that in a circle, equal chords subtend equal arcs.
⇒ arc AC = arc AD = x (let) ……………………(1)
∴ Reason (R) is true.
AB is a diameter of the circle.
As we know that the diameter of a circle divides the circle into two equal arcs.
⇒ arc ACB = arc ADB.
⇒ arc AC + arc BC = arc AD + arc DB.
From equation (1), we get :
⇒ x + arc BC = x + arc DB.
⇒ arc BC = arc DB.
∴ Assertion (A) is true.
∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
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Related Questions
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