Question

Using only ruler and compasses, construct a $\Delta$ABC in which BC = 6cm, $\angle$ABC = 120${}^{\circ }$ and AB = 3.5 cm. Now, with BC as diameter, draw a circle. Find a point P on the circumference of the circle such that it is equidistant from AB and BC. Then the measure $\angle$BCP is

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

Answer 1

The correct option is B

30^°

Steps of construction:

• Draw BC = 6 cm.
• Taking B as the centre, draw an angle of 120° .
• Join BF and produce it to X. Taking B as centre and AB = 3.5 cm as radius, draw an arc cutting BX at A. Join AC to get $\Delta$ABC.
• Draw perpendicular bisector of BC at M. With M as centre and radius BM, draw the circle with BC as a diameter.
• Draw angle bisector of $\angle$ ABC which intersects the circle at P.

P is the required point

• Join CP.

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