Question

a picture of these three.

(a) Circumcentre : Draw perpendicular bisectors of the three sides. The point where they meet is the Circumcentre. (b) Orthocentre : Draw the perpendiculars from the third vertex for each of the three sides. The point where they meet is the Orthocentre. (c) Incentre : Draw angle bisectors for each of the three angles. The point where they meet is the Incentre.

Answer 1

Steps to Construction of Circumcentre-

1.Draw the perpendicular bisector of the side AB.

2.Draw the perpendicular bisector of the side BC.

3.Draw the perpendicular bisector of the side AC.

4.Mark the point of intersection as 'O' which is circumcentre.

Steps to construction-

1. Set the compass width to the length of a side of the triangle.

2.From B draw an arc across AC creating point F.

3. From C draw an arc across BA creating point P.

4. Set the compass width to more than half the distance BP.

5. From B and P, draw arcs that intersect at point Q.

6. With a straightedge on C and Q, draw an altitude of the triangle.

7. Set the compass width to more than half the distance CF.

8. From C and F, draw arcs that intersect at point E.

9. With a straightedge on B and E, draw another altitude of the triangle.

The intersection of the altitudes is the orthocenter of the triangle

Steps to construction for incentre:

1. With the compass on a vertex, adjust its width to a medium setting.

2. Draw an arc across each leg.

3. Draw two intersecting arcs, one from each previous arc.

4. Draw the angle bisector line.

5. Repeat for the other vertices.

The point where these bisectors intersect will be the incentre.