Mathematics
Draw an isosceles ΔABC in which base BC = 6 cm and the altitude from vertex to the base is 4 cm. Draw its inscribed circle.
Answer
Steps of construction :
Draw BC = 6 cm as base.
At C, draw a perpendicular line CX and from it, cut off CE = 4 cm.
From E, draw EY, perpendicular to CX.
Draw perpendicular bisector of BC that intersects EY at A, such that AB = AC.
Join AB and AC to form △ABC.
Construct the angle bisector BH and IC of ∠ABC and ∠ACB respectively.
Let the two angle bisectors intersect at point P.
From P, draw PN perpendicular to the side BC.
With P as centre and radius equal to PN, draw a circle. The circle so drawn touches all the sides of the △ABC, and is the required incircle of △ABC.
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