Question

Construct a triangle ABC with ∠ABC = 60°, AB = 6 cm and BC = 5 cm. Extend side AB to a point D so that AD = 9 cm. Also, extend side AC to a point E so that AE = 8 cm. Construct a circle which must touch AB produced, BC and AC produced.

Answer 1

Steps of Construction:

1. Draw a line segment AB = 6 cm.
2. At point B, construct an angle of 60° with BA.
3. On this ray, mark point C such that BC = 5 cm.
4. Join AC. Thus, △ABC is constructed.
5. Produce AB beyond B. On the produced line, mark point D such that AD = 9 cm.
6. Produce AC beyond C. On the produced line, mark point E such that AE = 8 cm.
7. Since the required circle touches AB produced, BC, and AC produced, it is the excircle opposite vertex A.
8. Draw the external angle bisectors of ∠B and ∠C. Let them intersect at point O.
9. From O, draw a perpendicular to BC, meeting BC at P.
10. With centre O and radius OP, draw a circle. The circle so obtained touches AB produced, BC, and AC produced.