I think there is missing information in the question. ED should be parallel to OA

Yeah, I think there are also other missing information from this qn.. unable to solve part iii

The question will be solvable if it is assumed that OA // ED.

Edit : solvable using similar triangles without this assumption.

a iv) is actually solvable without this assumption.

b) should be that they are collinear/lie on same line.

c i) uses the concept of similar triangles

cii) is about the ratio of lengths for triangles with the same height, to find ratio of areas.

could you show me how? For part aiii)

Assume that OC // ED.

Then OA // ED since O, A and C are on the same line.

AD // OB (given)

Then AD // OE since O, E and B are on the same line.

Since AD // OE, and OA // ED,

ADEO is a parallelogram.


So AD and OE are not only parallel ,but equal in length as well.

Since they have the same magnitude and direction, vector AD = vector OE


Now, we use similar triangles.

Angle CAD = Angle COB
(Corresponding angles, AD // OB)

Angle CDA = Angle CBO
(Corresponding angles, AD // OB)

By AA similarity, △ COB and △ CAD are similar



So, if AC/OC = 2/3, then AD/OB also = 2/3
(This is known as the side splitter theorem, which uses the idea of similar triangles)

So AD = 2/3 OB

And therefore vector AD = ⅔ vector OB
= ⅔b

Since vector AD = vector OE, then vector OE also = ⅔b


Then, vector CE = vector OE - vector OC

= (⅔b - a)

Edit : (⅔b - 3a)

So sorry ahahahaha but those points still don’t get me to solve CE ;/

Haha was still updating and editing the answer. Do check out the latest update for the above comment. Hope it helps

WOW!! that’s incredible the way you derived everything! Understood, thank you so much!

btw, side splitter theorem, is that new? I haven’t heard of that term before!

Most welcome. If you need help for the rest let me know.

The term 'Side splitter theorem' isn't used in our local O Level syllabus, but it basically uses the idea of similar triangles.

Correction : It applies for the intercepted sides only, i.e

CD/DB = CA/AO

It doesn't cover the bottom lines in the caae of this question.

Ahhh I see! Okay sure! :)

Hi, so CE= CO + OE which would be -3a+ 2/3b, not a.. thank you so much again!

Yup welcome again