Incentre and circumcentre are same points
Steps for construction:
1. Construct triangle
ABC with
AB=BC=CA=6 cm.
2. To draw incircle:
a. Bisect any two angles and let the angle bisectors meet at
I.
b. From I, draw a perpendicular on
BC meeting at point
P.
c. With I as centre and IP as radius, draw a circle.
3. To draw circumcircle:
a. Draw the perpendicular bisectors of any two sides of the triangle
ABC.
b. Mark the point of intersection of the perpendicular bisectors as 0
C. Taking
OA or
OB or
OC as radius, draw a circle.
Now, observe that 0 and I are the same points. So, the incentre and circumcentre are same points. Also, take a
ruler and measure the radii of both circles that is IP and OA. You will see that
OA=2IP.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1727228/original_17.png)