Circle Question

[kazemagic]

How do you do this question?

Any help would be appreciated.
Thanks!

[Timske]

1. Find the area of the two sectors, add them together.

2. Find the area of the trapezium.

3. area of trapezium minus area of the sectors.

[kazemagic]

Yea I thought of that too, but I can't find the unkown angle to find the sectors lol...
BTW can I assume that the lines drawn to A and B are perpendicular to it?

[Timske]

Ah you cant find the angle because you are only given the radius, have to find another approach

[Carrotsticks]

I did it in degrees since your profile says HSC 2014 ie: You don't know radians yet (but it would have made the working out nicer).

[Timske]

Yea I thought of that too, but I can't find the unkown angle to find the sectors lol...
BTW can I assume that the lines drawn to A and B are perpendicular to it?

yes

[qwerty44]

Yea I thought of that too, but I can't find the unkown angle to find the sectors lol...
BTW can I assume that the lines drawn to A and B are perpendicular to it?

Yes you can. When the radius touches the point of contact of the tangent, it is perpendicular to the tangent.

[kazemagic]

Ah! Thanks carrotsticks so smart :O it never came across to my mind DC would be the addition of 2 radii lol

Also, thanks guys for your input

[Sanjeet]

Yes you can. When the radius touches the point of contact of the tangent, it is perpendicular to the tangent.

That's 3u

[qwerty44]

That's 3u

But the question can't be answered without that assumption, regardless of which course it is taught in.

[RealiseNothing]

But the question can't be answered without that assumption, regardless of which course it is taught in.

It can be done without that theorem. You just have to construct a line that meets the two radii at right angles (like carrot has done).

[Magical Kebab]

I did it in degrees since your profile says HSC 2014 ie: You don't know radians yet (but it would have made the working out nicer).

beast

[Sanjeet]

But the question can't be answered without that assumption, regardless of which course it is taught in.

Carrotsticks just did...

[kazemagic]

That's 3u

O_O i thought circle geometry is year 10 lol?

[RealiseNothing]

O_O i thought circle geometry is year 10 lol?

Some schools do it in year 10, but it's really only the basics iirc. You learn it in more depth in 3U.

[Sanjeet]

O_O i thought circle geometry is year 10 lol?

Lol no it's in the 3u prelim course

[kazemagic]

O_O that's weird I would have sworn that radii touching tangent thing theorem was in mathscape year 10 lol...

[RealiseNothing]

Lol no it's in the 3u prelim course

It can be done in year 10 5.3 at the end of the course.

[qwerty44]

Carrotsticks just did...

Oops. My mistake, sorry!

[Demento1]

It can be done in year 10 5.3 at the end of the course.

Actually, a capable student in year 9 could probably do it. I recall it being in the AMC paper on intermediate level.

[RealiseNothing]

Actually, a capable student in year 9 could probably do it. I recall it being in the AMC paper on intermediate level.

I meant, some schools do it at the end of the 5.3 course. As in, it's in the optional part of the syllabus.

But I agree, a capable student could do it a lot earlier, similar to the basics of complex numbers - they can be done in year 8 imo.