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A circle passes through two diagonally opposite vertices of a 3-inch by 4-inch rectangle. What is the least possible distance between the center of the circle and a vertex of the rectangle? Express your answer as a common fraction.

 May 16, 2020
 #1
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A circle passes through two diagonally opposite vertices of a 3-inch by 4-inch rectangle. What is the least possible distance between the center of the circle and a vertex of the rectangle? Express your answer as a common fraction.

 

 The least possible distance between the center of the circle and a vertex of the rectangle is  7/10 smiley

 May 17, 2020
 #2
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O is the center of a circle

 

M is a midpoint of a diagonal BD

 

tan(BDC) = 3/4        angle BDC = 36.86989765º

 

Angles  BDC, BNM, and CNO are congruent

 

BN = MB / sin(BNM)  = 4.166666666

 

CN = BN - BC  =  1.1666666666

 

OC = sin(CNO) * CN  = 0.7   or   7/10   indecision

 

Dragan  May 17, 2020
edited by Dragan  May 17, 2020
edited by Dragan  May 17, 2020

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