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.
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(ii) points equidistant from BA and BC.
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