Question

C and D are two points on AB and OB respectively such that AC:AB=1:3 and OD:OB=2:5. Let OA =a and OB =b.
(a) express OC and AD in terms of a and b
(b)AD intersect CO at E such that AE:AD = 1:m and OE:OC = 1:n. Find the values of m and n
My problem is that how to set the 2 equations for (b) so that i can solve for m and n?

Answer 1

Here's the diagram. It is a vector question..

Answer 2

Is AD a median and OC an altitude?

Answer 3

OD:OB = 2:5, so i don't think AD is the median

Answer 4

actually, both are not mentioned in the question

Answer 5

I can't write the vector notation(arrow on top), so I writing it the regular way.
OA=a
OD=2b/5
AD=OA+OD(Vectorically)

Answer 6

my mistake sorry

Answer 7

Oh yes that it should be. It was my mistake.

Answer 8

but what's next?

Answer 9

Do you need AD in vector form? Then just substitute the values of AO and OD...

Answer 10

i've solved part a already. My problem is that how to set the 2 equations for (b) so that i can solve for m and n?

Answer 11

Well, I am working on that part too. Have you tried:
AD=AE+ED
OC=OE+EC
We know the values of AD and OC. Now find AE and ED in terms of AD, I found it:
AE=AD/m
ED=(m-1)AD/m
Similarly, do so for OE and EC in terms of OC. Then add the above two equations and see what you get.
I will post as soon as I get an update on this.

Answer 12

i'm working on OE +ED = OD and AC+CE=AE but seems to be very complicated

Answer 13

if you add AE=AD/m and ED=(m-1)AD/m together, probably, you'll get AD=AD

Answer 14

try to add AE and AC instead. and also OE and OD

Answer 15

then, that's quite similar to my method

Answer 16

My workings for this question is on the right hand side.. Can you check it for me?

Answer 17

It's correct. Good work.

Answer 18

Thank you