The side AC of a triangle ABC is produced to E so that CE = 1/2 AC .D is the midpoint of BC and ED produced meets AB at F .Lines through D and C are drawn parallel to AB which meet AC at P and EF at point R respectively. prove that:
1) 3DF = EF
2) 4CR = AB

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In the given figure, side BC of $Δ A B C$ is bisected at D and O is any point on AD, BO and CO produced meet AC and AB at E and F respectively, and AD is produced to X so that D is the midpoint of OX. Prove that AO : AX = AF : AB and show that EF || BC.

Q. State true or false:

The side

A C

of a triangle

A B C

is produced to point

E

so that

C E = \frac{1}{2} A C

D

is the mid-point of

B C

and

E D

produced meets

A B

F

. Lines through

D

and

C

are drawn parallel to

A B

which meet

A C

at point

P

and

E F

at point

R

respectively. Hence,

3 D F = E F

The side AC of triangle ABC is produced to D so that CD=AC/2. If E is the mid point of BC and DE is produced to meet AB at F and EQ||AB, prove that EF=1/3DF

Q. The side