Question

In the figure Mis the midpoint of side BC.Angle AMB is obtuse and angle AMC is acute,seg AD is perpendicular to side BC then,a)with application of pythagoras theorem to obtuse angled triangle AMB,find AB square.​

Answer 1

AB² = BM² + AM² + BC.MD

Step-by-step explanation:

See the diagram attached.

Given that M is the midpoint of side BC of triangle Δ ABC.

So, BM = CM.

Now, AD is perpendicular to BC.

Now, taking the right triangle Δ ABD, we can apply the Pythagoras Theorem as,

AB² = AD² + BD²

⇒ AB² = (BM + MD)² + AD²

⇒ AB² = BM² + MD² + 2.BM.MD + AD²

⇒ AB² = BM² + (MD² + AD²) + 2.BM.MD

⇒ AB² = BM² + AM² + BC.MD {Since, BC = 2 × BM} (Answer)