Assertion: In a circles of radius 13 cm, there is a chord of length 10 cm at a distance of 12 cm from the centre of the circle.
Reason: A unique circle can be drawn to pass through three give non-collinear points.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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Solution

(b) Both the assertion and the reason are true, but the reason is not a correct explanation of the assertion.
Clearly, reason (R) is true.
Assertion (A):
OA = 13 cm and OL = 12 cm

AL² = OA² - OL²
⇒ AL² = (13)² - (12)² = (169 - 144) = 25
⇒ AL = 5 cm
⇒ AB = 2 × AL = 10 cm
Thus, assertion (A) is true.
∴ Reason (R) and assertion (A) are both true, but reason (R) does not give assertion (A).

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