If-A-and-B-are-two-points-in-the-plane-of-a-circle-having-radius-r-and-mAB-gt-2r-prove-that-at-least-one-of-A-or-B-is-outside-the-circle-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 25350 by Rasheed.Sindhi last updated on 08/Dec/17

If A and B are two points in the plane of a circle having radius r and mAB>2r ,prove that at least one of A or B is outside the circle.

$$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{points}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{having} \\ $$$$\mathrm{radius}\:\mathrm{r}\:\mathrm{and}\:\mathrm{mAB}>\mathrm{2r}\:,\mathrm{prove}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{A}\:\mathrm{or}\:\mathrm{B}\:\mathrm{is}\:\mathrm{outside}\:\mathrm{the}\:\mathrm{circle}. \\ $$

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