Question

Using a ruler and compasses only:
(i) Construct a triangle ABC with the
following data:
AB = 3.5 cm, BC = 6 cm and ZABC = 120°.
(ii) In the same diagram, draw a circle 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.
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Answer 1

Steps of constructions:

(a) Draw a line segment BC = 6 cm.

(b) At B, draw a ray BX making an angle of 120o with BC.

(c) From point B cut an arc of radius 3.5 cm to meet ray BX at C.

(d) Join AC.

ABC is the required triangle.

(ii)

(a) Bisect BC and draw a circle with BC as diameter.

(b) Draw perpendicular bisectors of AB. Let the two bisectors meet the ray of angle bisector of ABC at point P. P is equidistant from AB and BC.

(iii) On measuring BCP = 30