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Question
- Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.
- Find its in centre and mark it I.
- With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle. What is the length of the radius of this circle.
Solution
Steps of construction:
- Draw a line segment BC = 6 cm.
- With centre B and radius 8 cm draw an arc.
- With centre C and radius 5 cm draw another arc which intersects the first arc at A.
- Join AB and AC.
ΔABC is the required triangle. - Draw the angle bisectors of ∠B and ∠A intersecting each other at I. Then I is the incentre of the triangle ABC.
- Through I, draw ID ⊥ AB.
- Now from D, cut off `DP = DQ = 2/2 = 1 cm`.
- With centre I and radius IP or IQ, draw a circle which will intersect each side of triangle ABC cutting chords of 2 cm each.
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