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Statement-1: The common chord of the cir...

Statement-1: The common chord of the circles `x^(2)+y^(2)=r^(2)` is of maximum length if `r^(2)=34`.
Statement-2: The common chord of two circles is of maximum length if it passes through the centre of the circle with smaller radius.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, statement-2 is true.
The common chord of the given circles is `10x-16-r^(2)=0`
This will be of maximum length if it passes through the centre of the circle `x^(2)+y^(2)-10x+16=0` i.e. (5, 0).
`:. 50-16-r^(2)=0 rArr r^(2)=34`
So, statement-1 is true. Also, statement-2 is a correct explanation for statement-1.
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