37. Two circles are said to be orthogonal if the radius drawn from one of the circles to a point of intersection is perpendicular, at that point, to the radius drawn from the other circle. Prove that if two orthogonal circles have two points of intersection, the radii are perpendicular at both points of intersection.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
37. Two circles are said to be orthogonal if the radius drawn from one of
the circles to a point of intersection is perpendicular, at that point, to
the radius drawn from the other circle. Prove that if two orthogonal
circles have two points of intersection, the radii are perpendicular at
both points of intersection.
Transcribed Image Text:37. Two circles are said to be orthogonal if the radius drawn from one of the circles to a point of intersection is perpendicular, at that point, to the radius drawn from the other circle. Prove that if two orthogonal circles have two points of intersection, the radii are perpendicular at both points of intersection.
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