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Question
Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and measure its radius.
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Solution
Steps of construction:
- Draw a line segment BC = 4 cm.
- At C, draw a perpendicular line CX and from it, cut off CE = 2.5 cm.
- From E, draw another perpendicular line EY.
- From C, draw a ray making an angle of 45° with CB, which intersects EY at A.
- Join AB.
- ΔABC is the required triangle.
- Draw perpendicular bisectors of sides AB and BC intersecting each other at O.
- With centre O, and radius OB, draw a circle which will pass through A, B and C.
Measuring the radius OB = OC = OA = 2 cm.
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