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Another Gcse Circle
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Firstly, determine the radius OA of the circle. Note; given a coordinate on the circumferenc
15:21 Tue 28th Mar 2023
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.
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.
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.
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
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
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