Question

Construct ΔNTS where NT = 5.7 cm, TS = 7.5 cm and ∠NTS = 110° and draw incircle and circumcircle of it.

Answer 1

Rough figure:

Steps of construction:

For incircle:

1. Construct ΔNTS of given measures.
2. Draw bisectors of two angles, ∠T and ∠S.
3. Name the point of intersection of angle bisectors as I.
4. Draw a perpendicular IM on side TS. Point M is the foot of the perpendicular.
5. Draw a circle that touches all sides of the triangle with I as centre and IM as radius.

For circumcircle:

1. Draw the perpendicular bisectors of side NT and side TS of the triangle.
2. Name the point of intersection of the perpendicular bisectors as point C.
3. Join seg CN.
4. Draw circle with centre C and radius CN.