Question

if an equilateral triangle circumscribed a circle of radius 4 cm ,find the length of each side of the triangle
​

Answer 1

Answer:

Step-by-step explanation:

Given △ABC is a equilateral triangle inscribed in a circle.

Since, △ABC is a equilateral triangle,

∠C=60

Using the property, Angle subtended by same arc to centre of circle is twice the angle subtended by same arc to any point on the circle.

∴∠AOB=2×∠C

=2×60=120

Drawing perpendicular line from centre O to AB.

Using the property, A perpendicular line joining centre and chord bisects the chord and angle at centre.

∴AD=BD=x

∠AOD=∠BOD=60

In △AOD,

∠OAD+∠AOD+∠ODA=180                     (Angle sum property of a triangle)

or,90+60+∠OAD=180

or,∠OAD=180−90−60

=30

Now, In △AOD,

cos30=  

4

x

​

 

or,  

2

3

​

 

​

=  

4

x

​

,

or,x=  

2

4  

3

​

 

​

=2  

3

​

 

or,AD=BD=2  

3

​

 

or,AB=2×2  

3

​

=4  

3

​

 

Side of equilateral triangle =4  

3

​

 

∴ m=3