Question

Using a ruler and compasses only :

(i) Construct a triangle ABC with the following data :

AB = 3.5 cm, BC = 6 cm and $\angle ABC={120}^{\circ }$

(ii) In the same diagram draw a cricle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure $\angle BCP.$

Answer 1

1). Steps of Constructions :
(1) Draw a line segment BC = 6 cm
(2) Construct angle XBC = 120° at B
(3) With B as centre and radius 3.5 cm cut off AB = 3.5 cm
(4) Join AC
ABC is our required triangle.

2).
(1) Draw perpendicular bisector of BC which cuts BC at point D.
(2) With D as centre and radius = CD draw a circle passing through points B and C.
(3) Draw angle bisector of angle ABC which intersects the circle at point P.
(4) P is the point which is equidistant from AB and BC.

(3)using a protractor, measure $\angle BCP$ placing it along BC with zero at C

Theoretically $\angle BCP$ =180 -( $\angle BPC$ +$\angle PBC$ )

$\angle BCP$ =180 -(90 + 60 )

$\angle BCP={30}^0$