Mathematics
Using a ruler and compasses only :
(i) Construct a triangle ABC with the following data :
AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
(ii) In 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 ∠BCP.
Answer
Steps of construction :
Draw a line 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, cut off AB = 3.5 cm.
Join AC. ABC is the required triangle.
Draw perpendicular bisector of BC which cuts BC at point O. With O as center and radius = OB, draw a circle.
Draw angle bisector of ∠ABC which meets the circle at point P. Thus, point P is equidistant from AB and BC.
Measure ∠BCP.
Hence, ∠BCP = 30°.
Related Questions
Draw an inscribing circle of regular hexagon of side 5.8 cm.
Using a ruler and a compass, construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of :
(i) points equidistant from AB and AC.
(ii) points equidistant from BA and BC.
Hence construct a circle touching the three sides of the triangle internally.
Construct a triangle ABC in which base BC = 5.5 cm, AB = 6 cm and ∠ABC = 120°.
(i) Construct a circle circumscribing the triangle ABC.
(ii) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :
(i) a circle of radius 2.5 cm, passing through A and C.
(ii) construct two tangents to the circle from the external point B. Measure and record the length of the tangents.