Draw the circumcircle for

i. an equilateral triangle of side 6cm.

ii. an isosceles right triangle having 5cm as the length of the equal sides.

i. An equilateral triangle has all its angles 60°.

Rough Diagram:

Construction Steps:

Step 1: Draw the ΔABC with the given measurements.

Step 2:

We know that the circum centre of an acute angled triangle lies inside the triangle.

Construct the perpendicular bisector of any two sides (BC and AC) and let them meet at S which is circum centre.

Step 3: With S as centre and SA = SB = SC as radius draw the circum circle to pass through A, B and C.

∴ The required circum circle for the given triangle is drawn above.

ii. Let ∠A be 90° in an isosceles right triangle and AB and AC be the equal sides having length 5 cm.

Rough Diagram:

Construction Steps:

Step 1: Draw the ΔABC with the given measurements.

Step 2:

We know that the circum centre of a right angled triangle is at the midpoint of its hypotenuse.

Construct the perpendicular bisector of any two sides (AC and AB) and let them meet at S which is circum centre.

Step 3: With S as centre and SA = SB = SC as radius draw the circum circle to pass through A, B and C.

∴ The required circum circle for the given triangle is drawn above.