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# Geometry

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An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the distance between the center of the circle and the base?

May 29, 2021

#1
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Melody, CPhill, and Tigsy already did an amazing job answering this problem. :))

https://web2.0calc.com/questions/math_51432

=^._.^=

May 29, 2021
#2
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THX, catmg.....I didn't even remember  this one   !!!!   May 29, 2021
#3
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I just thought of a nice different solution, so I'll post it here. :))

I'm going to refrence Melody's graph since I'm not sure how to make my own yet.

Note than if you split this triangle in half, you get a 3, 4, 5 traingle.

The point (3, 4) a.

The point (0, 0) b.

The point (6, 0) c.

The point (3, 0) d.

And the center C.

Since aC = r, Cd = 4 - r.

bC = r too.

By pythagreon

(4-r)^2 + 3^2 = r^2

r^2 - 8r + 16 + 9 = r^2

8r = 25

r = 25/8

=^._.^=

May 29, 2021
#4
+2

This isn't EXACTLY  the  same  problem, but  you  can use  the  answer that catmg  referenced   to  find  the  distance  between  the center of  the  circle  and the  base  as

sqrt  ( 3.125^2  - 3^2)  =

0.875  units   May 29, 2021
#5
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Oh oops, I didn't realize it was a different problem.

But the same solutions still apply. :))

Distance formula is so smart.

=^._.^=

catmg  May 29, 2021
#6
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NP, catmg....I'm  just glad  you found  the original problem....!!!!   CPhill  May 29, 2021
#7
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An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the distance between the center of the circle and the base?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

BC = 5      MC = 3         BN = 2.5

BM = sqrt(52 - 32)

BM / BC = BN / BO        BO = 3 1/8

OM = BM - BO = 7/8 May 29, 2021