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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
avatar+1893 
+1

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

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

 

=^._.^=

 May 29, 2021
 #2
avatar+120075 
+1

THX, catmg.....I didn't even remember  this one   !!!!

 

cool cool cool

 May 29, 2021
 #3
avatar+1893 
+1

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. 

Let's call the radius r. 

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. 

ad = 3. 

 

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
avatar+120075 
+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

 

cool cool cool

 May 29, 2021
 #5
avatar+1893 
+1

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
avatar+120075 
+1

NP, catmg....I'm  just glad  you found  the original problem....!!!!

 

cool cool cool

CPhill  May 29, 2021
 #7
avatar+1300 
+3

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

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