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Question
Draw an isosceles triangle with sides 6 cm, 4 cm, and 6 cm. Construct the incircle of the triangle. Also, write the steps of construction.
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Solution
Steps of construction:
- Draw a line segment AB = 4 cm.
- With A as the centre and radius = 6 cm, draw an arc.
- With B as centre and radius = 6 cm, draw another arc intersecting the previous arc at point C.
- Join A to C and B to C. Then, △ABC is the required isosceles triangle (AC = 6 cm, BC = 6 cm, AB = 4 cm).
- Draw the bisector of angle ∠CAB.
- Draw the bisector of angle ∠CBA. These angle bisectors intersect at point O. Then O is the incentre of △ABC.
- Draw OP ⟂ AB. (From O, drop a perpendicular to the base AB.
Let the foot of the perpendicular be P.) - With O as centre and radius = OP, draw a circle touching all three sides of the triangle. This is the required incircle of △ABC.
- By measurement, OP gives the radius of the incircle.
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