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Question

# Assertion :Circles x2+y2=4 & x2+y2−8x+7=0 intersect each other in two distinct points. Reason: Circles with centres c1 & c2 and radius r1 & r2 intersect at two distinct points if |r1−r2|<c1c2<r1+r2

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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertionx2+y2=4 ∴c1=(0,0),r1=2 x2+y2−8x+7=0 ∴c2=(4,0),r2=3 ∴|c1c2|=4 & |r1−r2|=1,r1+r2=5|r1−r2|<|c1c2|<r1+r2 i.e circles intersect⇒ Assertion (A) & Reason (R) are true & Reason (R) is correct explanation of Assertion (A)Ans: A

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