Question

Pretend you are explaining how to circumscribe a circle about a triangle to your younger brother/sister, parent or friend. Explain each step you took to construct the circumscribed circle.

Answer 1

The circumcircle of a triangle is the circle that passes through all three vertices of the triangle.

To construct, first establishes the circumcenter and then draw the circle.

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect.

Steps:

Step 1: Draw the triangle.

Step 2: Using any two sides of the triangle, draw the perpendicular bisector of the two sides.

Step 3: Locate the circumcenter (point M) which is the point of intersection of the bisectors.

Step 4: Using the circumcenter, locate the radius (r) of the circle, because the distance from the center of the circle to any of the triangle's vertices is the radius, construct a circle that will pass through all the three vertices of the triangle.

Step 5: From the circumcenter, draw a circle with radius (r), to pass through the vertices of the triangle.

Thus, the circle formed through the points A, B, C is the circumcircle.