+0  
 
0
62
2
avatar

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
avatar
+1

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
avatar+1076 
+1

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

19 Online Users

avatar
avatar
avatar