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Cross the Circle (Posted on 2010-05-23) Difficulty: 2 of 5
Points A, B, and C are on a unit circle with A and C as end points of a diameter. The midpoint of chord AB is M. If the lengths of chord AB and line segment MC are the same, what is that length?

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Solution SPOILER | Comment 1 of 3

 

ans:  AB=1.5118*R

S0L:

Let AM=x and MC=2x So SIN(angle MCB]=.5

In triangle MCB the angle C is 30  so the angle AMC  is 120.

Applying cos law to this triangle we get:

x+4x+2*x*2x*(1/2)=4R

7x=4R     
........    *4/7

4x=16*R/7

ans: AB=MC=2X=4*R/SQRT(7)=1.5118*R     or .7559*2R


  Posted by Ady TZIDON on 2010-05-23 13:27:29
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