Mathematics
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.
Constructions
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Answer
(i) Steps of construction :
Draw a line segment BC = 5.5 cm
From B draw a ray BX such that ∠XBC = 120°.
From B draw an arc of 6 cm cutting BX at A.
Join AC. ABC is the required triangle.
Construct perpendicular bisectors of AB and BC, such that they intersect at O.
With O as center and OA as radius draw a circle passing through A, B and C.
Hence, above is the required circumcircle of triangle ABC.
(ii) Steps of construction :
Draw perpendicular bisector of BC, such that it intersects the circle at D.
Join CD and AD. ABCD is the cyclic quadrilateral.
Hence, above is the required cyclic quadrilateral.
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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 :
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(ii) construct two tangents to the circle from the external point B. Measure and record the length of the tangents.
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.