Question

Draw on obtuse angled triangle. Draw all of its medians and show their point of concurrence.

Answer 1

Given: $∆$ABC is an obtuse angled tringle.

To construct: All medians of $∆$ABC and their point of concurrence (Centroid).


Steps of construction:

(i) Draw any obtuse angled triangle ABC, $\angle$C is an obtuse angle.

(ii) With A as centre and radius more than half of AC, draw arcs on both sides of AC.

(iii) With C as centre and radius more than half of AC, draw arcs on both sides of AC intersecting the arcs of step (ii) at points P and Q.

(iv) Join PQ intersecting AC at point Z.

(v) With A as centre and radius more than half of AB, draw arcs on both sides of AB.

(vi) With B as centre and radius more than half of AB, draw arcs on both sides of AB intersecting the arcs of step (ii) at points R and S.

(vii) Join RS intersecting AB at point X.

(viii) With B as centre and radius more than half of BC, draw arcs on both sides of BC.

(xi) With C as centre and radius more than half of BC, draw arcs on both sides of AC intersecting the arcs of step (ii) at points D and E.

(x) Join DE intersecting BC at point Y.

(xi) Join AY, BZ and CX intersecting at point G.

Thus, AY, BZ and CX are the required medians of $∆$ABC and point is their point of concurrence (Centroid.