Question
Using a ruler and compasses only:
(1) construct a triangle $A B C$ with the ffollowing data: $A B=3.5 cm , B C=6 cm$ and $\angle A B C=120^{\circ}$.
(2) In the same diagram, draw a circle with BV as diameter. find a point $P$ on the circumference of thge circle which is equidistant from $A B$ and $B C$.
(3) Mesure $\angle B C P$

Answer

Step of constructions: 
(1) Draw a line segment BC=6 cm.
At B, draw a ray BX making an angle of 120° with BC. with B as center and radius 3.5 cm, out off AB=3.5 cm. join AC
Thus, ABC is the required triangle. 
(2) Draw perpendicular bisector MN of BC at point O. With O as center and radius =OB, draw a cirde.
Draw angle bisector of ∠ABC which meets the circle at point P. Thus, point P is equidistant from AB and BC. 
(2) On mesuring, ∠BCP=30°

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