If segment mn is a diameter of a circle f,

Mohamed Mooney

Mohamed Mooney

Answered question

2022-06-19

If segment mn is a diameter of a circle f, and v is a fixed point on mn, for which point E on MN is the length FE minimized?

Answer & Explanation

victorollaa5

victorollaa5

Beginner2022-06-20Added 16 answers

Yes. The chord is just a distraction. For any point D inside a circle (other than the centre), the closest point to D on the circle is the point where the radial line from the centre through D meets the circle.
Davon Irwin

Davon Irwin

Beginner2022-06-21Added 5 answers

You are right. A proof would be: Let F be any other point on the arc (different from our candidate E). Let O be the center of the circle. Then we have
O D + D E = r a d i u s
whereas
O D + D F > O F = r a d i u s
(by the triangle inequality). Therefore, D E < D F.

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