Activity 2
Scalene triangle and circle.
1) Draw the three perpendicular bisectors of the three sides of the triangle.
2) Create the point of intersection of two bisectors. Name it P.
hint: right-click and select Rename.
3) Draw the circle with centre P, going through A.
4) Move points A, B or C and answer the questions.
Scalene triangle and circle
Question 1
By zooming in on point P , can you tell if the three perpendicular bisectors are concurrent? Note: When two or more lines pass through a single point, in a plane, they are concurrent with each other and are called concurrent lines.
Question 2
By zooming in on points A, then B, then C, can you tell if the circle passes through the three vertices of the triangle? Note: In this case the circle is said to be the circumscribed circle of the triangle.
Question 3
Compare the three lengths PA, PB and PC.