Question

Using ruler and compasses only:

i) Construct a $\Delta$ABC in which BC = 6cm, $\angle$ABC = 120${}^{\circ }$ and AB = 3.5 cm.

ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the $\angle$BCP.

• A. 60^°
• B. 30^°
• C. 45^°
• D. 50^°

Answer 1

The correct option is B

30^°

Steps of Construction

STEP I Draw BC = 6 cm.

STEP II Taking B as centre, draw an arc cutting BC to D.

STEP III Taking D as centre draw an arc of same radius cutting arc drawn in step II at E and then draw another arc of same radius taking E as centre. Suppose it cuts drawn in step II at F.

STEP IV Join BF and produce it to X. Taking B as center and AB = 3.5 cm as radius, draw an arc cutting BX at A. Join AC to get $\Delta$ABC.

STEP V Draw right bisector of BC to meet BC at m. With M as center and radius BM, draw the circle with BC as a diameter.

STEP VI Any point equidistant from AB and BC lies on the bisector of $\angle$ ABC. So, draw bisector of $\angle$ ABC cutting the circle drawn in step V at P. Clearly, P is the required point.

Join CP. On measuring, we find that $\angle$ BCP = 30${}^{\circ }$