Mathematics
Construct a triangle ABC, having given AB = 4.8 cm, AC = 4 cm and ∠A = 75°. Find a point P
(i) inside the triangle ABC
(ii) outside the triangle ABC
equidistant from B and C; and at a distance of 1.2 cm from BC.
Locus
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Answer
Steps of construction :
Draw a line segment AB = 4.8 cm.
At A, draw a ray AX making an angle of 75°.
Cut off AC = 4 cm from AX.
Join BC. ABC is the required triangle.
Draw two lines l and m parallel to BC at a distance of 1.2 cm
Draw the perpendicular bisector of BC which intersect l and m at P and P'.
(i) Hence, P is the point inside the triangle ABC which is equidistant from B and C; and at a distance of 1.2 cm from BC.
(ii) Hence, P' is the point outside the triangle ABC which is equidistant from B and C; and at a distance of 1.2 cm from BC.
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