9. Construct the circumcircle and incircle of an equilateral ∆ XYZ with side 6.3 cm.

9. Construct the circumcircle and incircle of an equilateral ∆ XYZ with side 6.3 cm.

8. Construct incircle of ∆SGN such that SG = 6.7 cm, ∠S = 70º, ∠G = 50º and draw incircle of ∆ SGN.

8. Construct incircle of  ∆SGN such that SG = 6.7 cm, ∠S = 70º, ∠G = 50º and draw incircle of  ∆ SGN.

7. Construct the incircle of ∆DEF in which DE = DF = 5.8 cm, ∠EDF = 65º.

Geometry Challenge: Constructing an Incircle

7. Construct the incircle of ∆DEF in which DE = DF = 5.8 cm, and ∠EDF = 65º.

Glossary of Terms

Incircle

The largest possible circle that can be drawn inside a triangle, touching all three sides without crossing them.

Triangle (∆)

A fundamental shape in geometry consisting of three straight sides and three angles.

Isosceles Triangle

A triangle that has two sides of equal length. In this problem, ∆DEF is isosceles because DE = DF.

Angle Bisector

A line or ray that divides an angle into two smaller, equal angles. The construction of an incircle relies on finding where these bisectors meet.

Incenter

The center point of a triangle's incircle. It is found at the intersection of the triangle's three angle bisectors.

6. Construct the incircle of ∆ STU in which, ST = 7 cm, ∠T = 120º, TU = 5 cm.

6. Construct the incircle of  ∆ STU in which, ST = 7 cm,  ∠T = 120º, TU = 5 cm.

5. Construct the incircle of ∆RST in which RS = 6 cm, ST = 7 cm and RT = 6.5 cm.

5. Construct the incircle of ∆RST in which RS = 6 cm, ST = 7 cm and RT = 6.5 cm.

4. Construct a right angled triangle ∆PQR where PQ = 6 cm, ∠QPR = 40º, ∠PRQ = 90º. Draw circumcircle of ∆ PQR.

4. Construct a right angled triangle  ∆PQR where PQ = 6 cm,  ∠QPR = 40º, ∠PRQ = 90º. Draw circumcircle of ∆ PQR.

3. Construct the circumcircle of ∆ KLM in which KM = 7 cm, ∠ K = 60º, ∠ M = 55º.

3.  Construct the circumcircle of  ∆ KLM in which KM = 7 cm, ∠ K = 60º, ∠ M = 55º.

2. Construct the circumcircle of ∆ SIM in which SI = 6.5 cm, ∠ I = 125º, IM = 4.4 cm.

2. Construct the circumcircle of  ∆ SIM in which SI = 6.5 cm,  ∠ I = 125º, IM = 4.4 cm.

IMPORTANT POINTS TO REMEMBER FOR CONSTRUCTING CIRCUMCIRCLE OF TRIANGLE.

1. A circle passing through the vertices of the triangle is called the circumcircle of a triangle.

2. Circumcentre can be obtained by drawing perpendicular bisectors of any two sides of a triangle.

3. The point of intersection of the perpendicular bisectors is called
circumcentre and it is equidistant from the vertices of the triangle.

The position of circumcentre depends upon the type of a triangle.

(i) If the triangle is an obtuse angled triangle, the circumcentre lies outside the triangle.

(ii) If the triangle is an acute angled triangle, the circumcentre lies inside the triangle.

(iii) If the triangle is a right angled triangle, the circumcentre lies on the midpoint of the hypotenuse.