Mathematics
Using a ruler and a compass, construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of :
(i) points equidistant from AB and AC.
(ii) points equidistant from BA and BC.
Hence construct a circle touching the three sides of the triangle internally.
Constructions
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Answer
Steps of construction :
Draw a line segment AB = 7 cm.
Construct AX such that ∠XAB = 60°.
With A as center and radius = 5 cm cut arc on AX and mark it as point C.
Join BC. ABC is the required triangle.
Draw AY and BZ, angle bisector of A and B.
Let AY and BZ meet at point O.
Draw OD ⊥ AB.
With O as center and OD as radius draw a circle.
(i) Hence, AY is the locus of points equidistant from AB and AC.
(ii) Hence, BZ is the locus of points equidistant from BA and BC.
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