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# Circle Geometry - Find the length of the Chord pq Watch

1. Can you please have a look at this for me.

A circle with centre C, has the equation X^2 + Y^2 -12X +6Y -20=0. Find the centre coordinates and radius.

C.T. Square gives (X -6)^2 + (Y+3)^2 = 65. c(6,-3)

Now: the origin is the mid point of a chord, show that the gradient of the chord is 2. The grad of 0C is - 1/2 therefore the gradient of the chord using M1xM2 =-1 does equal 2.

Now find the distance of o(0,0) to the centre. The distance is 3 root 5 ( 45 ^1/2). Can someone tell me how to find the length of the chord please? Thanks. Dominic
2. (Original post by van.domo)
Can you please have a look at this for me.

A circle with centre C, has the equation X^2 + Y^2 -12X +6Y -20=0. Find the centre coordinates and radius.

C.T. Square gives (X -6)^2 + (Y+3)^2 = 65. c(6,-3)

Now: the origin is the mid point of a chord, show that the gradient of the chord is 2. The grad of 0C is - 1/2 therefore the gradient of the chord using M1xM2 =-1 does equal 2.

Now find the distance of o(0,0) to the centre. The distance is 3 root 5 ( 45 ^1/2). Can someone tell me how to find the length of the chord please? Thanks. Dominic
You know that the radius of the circle is √65 and the distance from the origin to the centre is √45.
Here is a diagram:
So you now have a right angled triangle:
L/2 = √(64 + 45)
So L = 4
√5

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