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The centers of the circles touching both the coordinate axes lies on the line

x – y = 0 or x + y = 0 according to the quadrant in which the circle lies.

Based on this data answer the following 2 questions.

A) If the difference between the radii of the circles passing through (a, b) and touching the axes is c>0 and a, b > 0 then the least value of a + b is

B) If one of the points of intersection of the two circles touching the axes is (p,q) then the length of the common chord is

The centers of the circles touching both the coordinate axes lies on the line

x – y = 0 or x + y = 0 according to the quadrant in which the circle lies.

Based on this data answer the following 2 questions.

A) If the difference between the radii of the circles passing through (a, b) and touching the axes is c>0 and a, b > 0 then the least value of a + b is

B) If one of the points of intersection of the two circles touching the axes is (p,q) then the length of the common chord is

### Asked by Sunil Soni | 10th Aug, 2016, 07:07: PM

### As the circles touches the axes so, the point of intersection will always lie on axis.
So either x coordinate or y coordinate will be zero.
And the length of common cord will also bezero.
Only option (4) satisfies the above two conditions.
Please post one query at a time.

### Answered by Vijaykumar Wani | 12th Aug, 2016, 05:34: PM

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