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Question

# Construct a triangle ABC in which BC = 4 cm, ∠ACB=45∘ and perpendicular from A to BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and find its radius.

A

4 cm

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B

5 cm

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C

2 cm

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D

3 cm

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Solution

## The correct option is C 2 cm Steps of Construction: i) Draw a line segment BC = 4cm. ii) At C,draw a perpendicular CX and cut off CE = 2.5 cm. iii) From E,draw another perpendicular EY. iv) From C,draw a ray making an angle of 45∘ with CB,which intersects EY at A. v) Join AB. Triangle ABC is the required triangle. vi) Draw perpendicular bisectors of sides AB and BC intersecting each other at O. vii) With centre O,and radius OB,draw a circle which will pass through A. B and C. Measure the radius OB = OC = OA = 2 cm

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