Question

Construct $△$ABC such that BC = 7.8 cm , $\angle$BAC = 100$°$ and Median AM = 3.5 cm.

Answer 1

Steps of construction:
(i) Draw a line segment BC = 7.8 cm.
(ii) Through B, draw BY such that $\angle$CBY= 100$°$.
(iii) Draw BX$\perp$BY.
(iv) Draw the perpendicular bisector of BC intersecting BX at O and BC at M.
(v) With O as the centre and OB as the radius, draw a circle.
(vi) The minor arc BWC of the circle contains the vertical 100$°$
(vii) With M as the centre, draw an arc of radius 3.5 cm meeting the circle at A and A'.
Thus, $△$A'BC or $△$ABC is the required triangle.