Two circles X and Y with centres A and B intersect at C and D. If area of circle X is 4 times area of circle Y, then AB=?

Question

This question is solved by taking angleACB = 90 in my book. How can we say that this angle a right angle triangle? Given answer is √5r.

There must be a drawing that goes with this. The angle between a radius and the tangent at the point the radius hits the circle is a right angle, does that do what you need? Without further information I don't see how we answer this. — Ross Millikan, Jan 16 '19 at 08:12

score 0 · Answer 1 · answered Jan 16 '19 at 07:15

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You need information because you can put the circles so that it intersect and $AB$ can vary. I suppose that $\angle ACB =90^\circ$ is hypothesis.

answered Jan 16 '19 at 07:15

guchihe

273

Question is given with four option and in solution ACB=90 [ angle at the point of intersection to the center of the circles.] is written. – sk8 Jan 16 '19 at 07:30

score 0 · Answer 2 · answered Jan 16 '19 at 07:35

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By the triangle inequality $$AC+CB>AB$$ or $$2r+r>AB$$ or $$AB<3r.$$ Now, by the triangle inequality again we obtain $$AB+r>2r,$$ which gives $$r<AB<3r.$$

answered Jan 16 '19 at 07:35

Michael Rozenberg

194,933

Two circles X and Y with centres A and B intersect at C and D. If area of circle X is 4 times area of circle Y, then AB=?

2 Answers2