4)The centroid divides the median in the ratioa) 2:1b) 1:3d)3:1c)1:4

1.	4)The centroid divides the median in the ratioa) 2:1b) 1:3d)3:1c)1:4
Answer» A triangle ABC, AD, BE & CF Medians intersecting at O. O is the Centroid of the triangle. As medians bisect sides of the triangle. So, BD=DC, AF=FB, AE=EC, TO PROVE:● AO/OD = 2:1 CONSTRUCTION:● Extend OD = DH , Join H& C And B & H PROOF:● OD = DH ( by construction) BD = DC ( median AD bisects BC) Therefore, BHCE is a parallelogram Now, in triangle AHC, AE = EC ( given) OE // HC ( proved above) So, AO = OH ( Mid point theorem) => AO = 2OD => AO/OD = 2/1 (a) is correct option

Answer»

A triangle ABC, AD, BE & CF Medians intersecting at O. O is the Centroid of the triangle.

As medians bisect sides of the triangle.

So, BD=DC, AF=FB, AE=EC,

TO PROVE:● AO/OD = 2:1

CONSTRUCTION:● Extend OD = DH , Join H& C And B & H

PROOF:● OD = DH ( by construction)

BD = DC ( median AD bisects BC)

Therefore, BHCE is a parallelogram

Now, in triangle AHC,

AE = EC ( given)

OE // HC ( proved above)

So, AO = OH ( Mid point theorem)

=> AO = 2OD

=> AO/OD = 2/1

(a) is correct option

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