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555-605 (Medium)|   Geometry|      
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LamboWalker
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An equilateral triangle ABC, whose side is 6 cm is inscribed in a 17 Aug 2021, 04:25
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25% (medium)

Question Stats:

77% (01:42) correct 23% (01:24) wrong based on 62 sessions

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An equilateral triangle ABC, whose side is \(6\) cm is inscribed in a circle. Find the radius of the circle.


(A) \(2\)
(B) \(2\sqrt{3}\)
(C) \(3\)
(D) \(4\)
(E) \(3\sqrt{3}\)
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B
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Crytiocanalyst
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An equilateral triangle ABC, whose side is 6 cm is inscribed in a 17 Aug 2021, 22:39
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LamboWalker
An equilateral triangle ABC, whose side is \(6\) cm is inscribed in a circle. Find the radius of the circle.


(A) \(2\)
(B) \(2\sqrt{3}\)
(C) \(3\)
(D) \(4\)
(E) \(3\sqrt{3}\)
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let us divide the equilateral triangle into 6 sides
perpendicular to the side be x then area of one side =1/2*x*3(since the side is bisected in an equilateral triangle )

total area of the triangle 9x=3^1/2 * 6*6 /4
x=(3)^1/2

from each section of the triangle we get x^2 +9 =r^2
=>12=r^2
=>r=2*3(1/2)

Therefore IMO B
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An equilateral triangle ABC, whose side is 6 cm is inscribed in a 17 Aug 2021, 23:10
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Crytiocanalyst
LamboWalker
An equilateral triangle ABC, whose side is \(6\) cm is inscribed in a circle. Find the radius of the circle.


(A) \(2\)
(B) \(2\sqrt{3}\)
(C) \(3\)
(D) \(4\)
(E) \(3\sqrt{3}\)

let us divide the equilateral triangle into 6 sides
perpendicular to the side be x then area of one side =1/2*x*3(since the side is bisected in an equilateral triangle )

total area of the triangle 9x=3^1/2 * 6*6 /4
x=(3)^1/2

from each section of the triangle we get x^2 +9 =r^2
=>12=r^2
=>r=2*3(1/2)

Therefore IMO B
Show more

Would you be able to draw a diagram for your solution? Apologies, I’m unable to follow the beginning where you mention diving the triangle into 6 sides.

Thank you in advance

Posted from my mobile device
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Crytiocanalyst
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An equilateral triangle ABC, whose side is 6 cm is inscribed in a 18 Aug 2021, 00:03
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SurajC
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LamboWalker
An equilateral triangle ABC, whose side is \(6\) cm is inscribed in a circle. Find the radius of the circle.


(A) \(2\)
(B) \(2\sqrt{3}\)
(C) \(3\)
(D) \(4\)
(E) \(3\sqrt{3}\)

let us divide the equilateral triangle into 6 sides
perpendicular to the side be x then area of one side =1/2*x*3(since the side is bisected in an equilateral triangle )

total area of the triangle 9x=3^1/2 * 6*6 /4
x=(3)^1/2

from each section of the triangle we get x^2 +9 =r^2
=>12=r^2
=>r=2*3(1/2)

Therefore IMO B

Would you be able to draw a diagram for your solution? Apologies, I’m unable to follow the beginning where you mention diving the triangle into 6 sides.

Thank you in advance

Posted from my mobile device
Show more

https://www.google.com/url?sa=i&url=htt ... AdAAAAABAD

This is the intended diagram
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Amandhanani2627
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An equilateral triangle ABC, whose side is 6 cm is inscribed in a 18 Aug 2021, 00:22
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for equilateral triangle incenter=centroid=orthocenter,
so altitude=median= (3^1/2)/2 * a (a=6)
= 3*(3^1/2)

so, radius = (2/3)*(3*(3^1/2)) = 2*(3^1/2)
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parasma
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An equilateral triangle ABC, whose side is 6 cm is inscribed in a 18 Aug 2021, 01:59
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Area of a triangle inscribed in a circle

A= abc/4R

a,b,c are sides of a triangle and R is the radius of circle

So A= Root 3/4 a^2= 9 root 3

9 root 3= 216/4R

R= 54/9 root3
R= 6/ root 3
So R= 2 root3
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