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.
Constructions
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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°.
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Related Questions
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.
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.