Another Gcse Circle

[kuiperbelt]

TIA!!

https://ibb.co/W2nRkVd

[emeritus]

You will never progress in your course by posting questions where you haven't proposed your own thoughts to be analysed and questioned. So post your thoughts and principles on solving the problem. In that way you can be assisted in understanding the processes involved rather than just being given the solution.

[ClareTG0ld]

Questions like this annoy me because I can see every single step but also have to actually put pen to paper in order to get the numbers.

I'll post a more complete solution later, but this problem, like most of them of a similar type, is solved by finding right-angled triangles. You'll need to spot two of them.

[Buenchico]

I like the easy ones ;-)

https://postimg.cc/2b456qtq

[Atheist]

Buen; Isn't OA over OB sine 30?

[perseverer]

Buenchico

Tan30=OA/AB. ?

[ZebuSanctuary]

Firstly, determine the radius OA of the circle.

Note; given a coordinate on the circumference of a circle, where the radius and the tangent are both incident on that coordinate, there will exist an angle of 90° between the the 2 straight lines.

Applyling trigonometry;

Sin 30° = OA ÷ OB thus OA = 0.5 x OB which is OA = 0.5 x 20

Therefore Radius OA = 10

Now construct a right angled triangle (RAT) where OP is the Hypotenuse, the coordinate on the x axis is 3p hence the length of the adjacent side to angle POB. The coordinate 2p will form the opposite side to angle POB and also acts as the other length of the RAT.

Now apply Pythagoras Theorem;

OP² = (3p)² + (2p)² -----> 100 = 9p² + 4p²

thus p² = 100 ÷ 13 -------> p = √7.7 ---->

Answer p = 2.8 to 1 d.p

[bobbinwales]

Buenchico is right with his tan 30 as far as i can see. Just need to draw a line from q to A to make the oppasite side and its now a right angle triangle

[bobbinwales]

ignore me i meant wrong! its sine 30

[bobbinwales]

OB is the longest side Buenchico not the adjacent

[bobbinwales]

Looks like kuiperbelt has it

[bobbinwales]

typo again! I meant zebusanctuary has it!

[Etch]

ZebuSanctuary's answer is correct: p = √(100/13) = 2.8 to 1 decimal place

I can now see why Buenchico's avatar has a red face! :-D

[ClareTG0ld]

Buen's messed up Maybe it wasn't so easy after all :P

[kuiperbelt]

\Firstly, determine the radius OA of the circle\

My grandson and I got this far then didn't know what to do next LOL

Thank you all for your contributions!!