Question

Draw an equilateral triangle with sides equal to 6 cm. Construct the incircle and circumcircle for the triangle. Which of the following is true?

• A. Incentre and circumcentre are different points
• B. Radius of the circumcircle is four times the radius of the incircle
• C. Incentre and circumcentre are same points
• D. Radius of the circumcircle is equal to the radius of the incircle

Answer 1

The correct option is C

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 O

c. Taking OA or OB or OC as radius, draw a circle.

Now, observe that O 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.