Question

Construct a $\Delta$ABC in which BC$=5.5$cm, $\angle$A$={60}^o$ and the median AM from the vertex A is $4.5$cm.

Answer 1

In $\Delta$ABC, BC$=5.5$cm, $\angle$A$={60}^o$, Median AM$=4.5$cm.

Construction:

(i) Draw a line segment BC$=5.5$cm.

(ii) Through B draw BX such that $\angle$CBX$={60}^o$.

(iii) Draw BY$\perp$ BX.

(iv) Draw the perpendicular bisector of BC intersecting BY at O and BC at M.

(v) With O as centre and OB as radius, draw the circle.

(vi) The major arc BKC of the circle, contains the vertical angle ${60}^o$.

(vii) With M as centre, draw an arc of radius $4.5$cm meeting the circle at A and A'.

(viii) $\Delta$ ABC or $\Delta$A'BC is the required triangle.