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Question

# Assertion :The circle of smallest radius passing through two given points A & B must be of radius 12AB. Reason: A straight line is a shortest distance between two points.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

## The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for AssertionLet C1 be the circle passing through A and B whose diameter is AB and C2 be another circle which passes through A and B then center of C1 and C2 must lies on the ⊥ bisector of AB Indeed the center of C1 is mid point M of AB and center of any other circle lies somewhere else on the bisector. Then M1A>AM ( hypotenuse of right angle. ΔAMM1) ⇒ Radius of C2>12AB ⇒C1 is the circle whose radius is the least.Thus the Assertion is true but does not actually follow from reason which is certainly true.Hence, choice (B) is correct answer.

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