Question

In ∆ XYZ, M is the mid-point of YZ. MP and MQ are perpendiculars to XY and XZ respectively. If XY = XZ, prove that : i) PM=QM ii) XP=XQ

Answer 1

Answer:

Since M and N are the mid-points of XY and YZ respectively,

therefore by midpoint theorem,

MN is parallel to XZ and MN=

2

1

XZ=

2

1

XY (since XY=XZ)

or MN=MX=MY.

solution

Step-by-step explanation:

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Answer 2

Answer:

Let x/a = y/b = z/c = k, [By k method]

x = ak, y= bk and z=ck

L.H.S. = a3k3/a2 + b3k3/b2 + c3k3/c2 > k3[a + b + c]

R.H.S. = [ak + bk + ck]3/[a + b + c)2 → k3[a + b + c]3/[a + b + c)2

= k3(a + b + c)

L.H.S. = R.H.S. =

Hence proved.