GPREP DS#7

[hardikrs]

Figure attached.

For those who cannot see the figure.

It is a triangle with vertices A, B and C and there is point on D on side AC. B is connected to D. angle BAC = x and angle BDC and BCA = 2x. What is the length of BC?

1. Line segment AD has length = 6

2. X = 36

Please explain your answer.

[eravi11]

ok..
we know angle DAB= x and angle BDC=2x

And traingle property says that: angleDAB+angleABD=angle BDC
so angle ABD=x

statement 1:
Now if angle ABD and DAB are each equal to x, then AD=BD=6

since angle BDC=angleBCD=2x, thus BD=BC=6.
SUFFICIENT

statement 2 is only talking about angles..hence we can't find BC..INSUFFICIENT

choose A

[clock60]

agree with A
2x+2x+dbc=180 (from triangle dbc)
dbc=180-4x

adb+2x=180,
adb=180-2x

from triangle abc
x+2x+(180-4x)+abd=180
abd=x
it means that triangle adb isosceles (as angle bad=abd) and ad=db
as triangle bds also isosceles and has common side with adb all we need to know any side
(1) ad=6 so db=6 and db=bc=6 sufficient
(2) no values of the sides insufficient
so A