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Let G be the centroid of triangle ABC an...

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A
If AC = 1, then the length of the median of triangle ABC through the vertex A is equal to

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
C
Let `B(a,b), C(c,b), A (a,d)`.
Then D (mid point of BC) is `((a+c)/(2),b)`
E (mid point of AB) is `(a,(b+d)/(2))`
Given slope of `CE = 1 rArr (b-(b+d)/(2))/(c-a) =1rArr ((b-d))/(c-a) =2`
Slope of `AD = (b-d)/((a+c)/(2)-a) =2 ((b-d))/(c-a) =4`
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