im confused

[ashen coral]

asks what |DE| equals to

[elder shadow]

first of all, do you know the coordinates of D?

[ashen coral]

D is the point where the extension of OA touches x=1 line

cant know the exact coordinates

[elder shadow]

you can

let's take the point (1, 0) as Z for now, alright

now, in triangle ODZ, can you use some trigonometry to find the length ZD

[ashen coral]

it would be tanx

[elder shadow]

so, what's the coordinate of D?

[ashen coral]

(1, tanx)?

[elder shadow]

yes

now, what do you think is the angle ZOE

[ashen coral]

how can i find it

[elder shadow]

well, there are 2 tangents to the circle from E, so they should have equal lengths, divide the angle in the middle...

[ashen coral]

so its x/2

[elder shadow]

yup

so, what's the length ZE

[ashen coral]

its cotx((1÷cosx)-1)

i think

[elder shadow]

yes

now, can you find DE

[ashen coral]

give me a second

(sec²x-secx)/tanx

thank you so much ❤️

[elder shadow]

correcto!

[ashen coral]

im so relieved

but why (1-cosx)/cosx.sinx not in the answers lol