PLEASE HELP- C2 Coordinate Geometry

10. The circle C, with centre A, passes through the point P with coordinates (–9, 8) and the point Q with coordinates (15, –10).

Given that PQ is a diameter of the circle C,
(a) find the coordinates of A, (2)
(b) find an equation for C. (3)

A point R also lies on the circle C.
Given that the length of the chord PR is 20 units,
(c) find the length of the shortest distance from A to the chord PR.
Give your answer as a surd in its simplest form (2)
(d) Find the size of the angle ARQ, giving your answer to the nearest 0.1 of a degree. (2)

Confused on part c and d

Reply 1

emx_eco

OP

13

10. The circle C, with centre A, passes through the point P with coordinates (–9, 8) and the point Q with coordinates (15, –10).

Given that PQ is a diameter of the circle C,
(a) find the coordinates of A, (2)
(b) find an equation for C. (3)

A point R also lies on the circle C.
Given that the length of the chord PR is 20 units,
(c) find the length of the shortest distance from A to the chord PR.
Give your answer as a surd in its simplest form. (2)
(d) Find the size of the angle ARQ, giving your answer to the nearest 0.1 of a degree. (2)

I'm confused on part c and d :smile:

Reply 2

emx_eco

OP

13

The mark scheme said you have to find the length of RQ but I don't understand why :s-smilie:

Reply 3

emx_eco

OP

13

10. The circle C, with centre A, passes through the point P with coordinates (–9, 8) and the point Q with coordinates (15, –10).

Given that PQ is a diameter of the circle C,
(a) find the coordinates of A, (2)
(b) find an equation for C. (3)

A point R also lies on the circle C.
Given that the length of the chord PR is 20 units,
(c) find the length of the shortest distance from A to the chord PR.
Give your answer as a surd in its simplest form. (2)
(d) Find the size of the angle ARQ, giving your answer to the nearest 0.1 of a degree. (2)

I'm confused on part c and d :smile:

Reply 4

username3006294

14

Original post by emx_eco

10. The circle C, with centre A, passes through the point P with coordinates (–9, 8) and the point Q with coordinates (15, –10).

Given that PQ is a diameter of the circle C,
(a) find the coordinates of A, (2)
(b) find an equation for C. (3)

A point R also lies on the circle C.
Given that the length of the chord PR is 20 units,
(c) find the length of the shortest distance from A to the chord PR.
Give your answer as a surd in its simplest form. (2)
(d) Find the size of the angle ARQ, giving your answer to the nearest 0.1 of a degree. (2)

I'm confused on part c and d :smile:

Have you tried drawing it?

Reply 5

emx_eco

OP

13

Original post by em_lj

Have you tried drawing it?

yep, I still cant seem to see how the mark scheme has done it. This is the mark scheme: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C2/Papers-Edexcel/June%202014%20(R)%20MA%20-%20C2%20Edexcel.pdf
Question 10c

Reply 6

ghostwalker

17

Original post by emx_eco

10. The circle C, with centre A, passes through the point P with coordinates (–9, 8) and the point Q with coordinates (15, –10).

Given that PQ is a diameter of the circle C,
(a) find the coordinates of A, (2)
(b) find an equation for C. (3)

A point R also lies on the circle C.
Given that the length of the chord PR is 20 units,
(c) find the length of the shortest distance from A to the chord PR.
Give your answer as a surd in its simplest form. (2)
(d) Find the size of the angle ARQ, giving your answer to the nearest 0.1 of a degree. (2)

I'm confused on part c and d :smile:

Diagram if you haven't already.

c) Shortest distance fo A to PR, bisects PR. If we call the point X, then Pythagoras on PXA will let you find AX.

d) Don't see any need to work out RQ. You could use cosine rule on triangle PRA to find angle PRA, and then subtract from 90 to get angle ARQ (angle in a semicircle is 90)

Reply 7

username3006294

14

Original post by emx_eco

yep, I still cant seem to see how the mark scheme has done it. This is the mark scheme: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C2/Papers-Edexcel/June%202014%20(R)%20MA%20-%20C2%20Edexcel.pdf
Question 10c

Ahhh I see I don't do edexcel so I've never seen that type of question before, sorry I couldn't be of any help

Reply 8

Andrew Dawson

7

I have only a solution to part C. Basically, draw a triangle and use circle theorems.

Reply 9

emx_eco

OP

13

Original post by Andrew Dawson

I have only a solution to part C. Basically, draw a triangle and use circle theorems.

I partially understand it now- but if you don't know the coordinates of R then how do you know how to sketch the diagram. Because I ended up sketching my diagram differently which really confused me

Reply 10

Andrew Dawson

7

As it states PR is a chord. So you can conclude that R must lie on the circumference on the circle. Therefore, it must have a distance equal to the radius from the center A. You are told it has a distance of 20 units from P and P is on the circumference aswell. Meaning, that also has a distance equal to the radius. The shortest distance from A the chord PR is when it is perpendicular therefore bisecting the chord in half. Giving you a right angled triangle. From there is just Pythagoras.

Reply 11

emx_eco

OP

13

Original post by Andrew Dawson

As it states PR is a chord. So you can conclude that R must lie on the circumference on the circle. Therefore, it must have a distance equal to the radius from the center A. You are told it has a distance of 20 units from P and P is on the circumference aswell. Meaning, that also has a distance equal to the radius. The shortest distance from A the chord PR is when it is perpendicular therefore bisecting the chord in half. Giving you a right angled triangle. From there is just Pythagoras.

But if P has an x-coordinate of -9 and A has an x-coordinate of 3, then how can your diagram be sketched like that because the point P should be behind the point A?

Reply 12

mathshelppp

2

http://www.physicsandmathstutor.com/...s/c2-by-topic/

for edexcel c2
whats the difference between set 1 and set 2?
is set 1 just broken down into each topic??

anyone????

Original post by emx_eco

10. The circle C, with centre A, passes through the point P with coordinates (–9, 8) and the point Q with coordinates (15, –10).

Given that PQ is a diameter of the circle C,
(a) find the coordinates of A, (2)
(b) find an equation for C. (3)

A point R also lies on the circle C.
Given that the length of the chord PR is 20 units,
(c) find the length of the shortest distance from A to the chord PR.
Give your answer as a surd in its simplest form (2)
(d) Find the size of the angle ARQ, giving your answer to the nearest 0.1 of a degree. (2)

Confused on part c and d

(c) The shortest distance from the centre to any chord in a circle, is the perpendicular distance to it. So for your chord PR, the midpoint can be called M of it, and so AM would be the shortest distance to the chord. Since we have perpendicularity, all you need to do to find

AM

is take

\sqrt{r^2-(\frac{1}{2}PQ)^2}

(r is the radius, and obviously PM=RM since M is the midpoint of PR)

(d) ARQ is an isosceles triangle with lengths AR=AQ=r and also you have a right-angled triangle PRQ with PR=20 and PQ=diameter.

An quick sketch would help you understand that we have a situation whereby

PQ\sin(\angle PQR = \angle ARQ)=PR

so all you need is the angle which you can easily find by rearrangement.

(edited 6 years ago)

Reply 14

mathshelppp

2

http://www.physicsandmathstutor.com/...s/c2-by-topic/

for edexcel c2
whats the difference between set 1 and set 2?
is set 1 just broken down into each topic??

anyone????

@RDKGames

Original post by mathshelppp

http://www.physicsandmathstutor.com/...s/c2-by-topic/

for edexcel c2
whats the difference between set 1 and set 2?
is set 1 just broken down into each topic??

anyone????

@RDKGames

I don't know, I never did Edexcel nor did I use this site.

Reply 16

emx_eco

OP

13

Original post by mathshelppp

http://www.physicsandmathstutor.com/...s/c2-by-topic/

for edexcel c2
whats the difference between set 1 and set 2?
is set 1 just broken down into each topic??

anyone????

I'm not entirely sure either, All the questions from both sets seem relevant anyway so I would use either of them

Reply 17

Andrew Dawson

7

Original post by emx_eco

But if P has an x-coordinate of -9 and A has an x-coordinate of 3, then how can your diagram be sketched like that because the point P should be behind the point A?