Circle Tangent Gradient Worksheet A The worksheet is

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Lines around Circles ① Mark point A on the circle at (3, 3), then

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Circle – Tangent Gradient – Worksheet A The worksheet is in 2 sizes.

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Lines around Circles ① Mark point A on the circle at (3, 3), then draw line OA from the origin (O) to point A. What is the equation of line OA? ② Mark point B on the circle at (2, 4), & draw line OB from the origin. What is the gradient of the line OB? What is the gradient of a line perpendicular to OB? How are the gradients of these graphs related? Plot & label line CD - the line that is perpendicular to OB & passes through B. Draw & label the line that is parallel to CD & touches the circle at one point. Where on the circle will a tangent have a gradient of 2? ③ Sketch the line OD. D Find the equation of the tangent at (6, − 2) Find the gradient of this radius, is it positive or negative? . Find the equation of the tangent at (− 2, 6) ④

Lines around Circles ① Mark point A on the circle at (3, 3), then draw line OA from the origin (O) to point A. A What is the equation of line OA? ② Mark point B on the circle at (2, 4), & draw line OB from the origin. C B What is the gradient of the line OB? 2 D How are the gradients of these graphs related? Perpendicular tangent What is the gradient of a line perpendicular to OB? Plot & label line CD - the line that is perpendicular to OB & passes through B. Draw & label the line that is parallel to CD & touches the circle at one point. Where on the circle will a tangent have a gradient of 2? ③ Sketch the line OD. D (4, − 2) (− 4, 2) Find the equation of the tangent at (6, − 2) Find the gradient of this radius, is it positive or negative? . Find the equation of the tangent at (− 2, 6) ④

Lines around Circles ① Mark point A on the circle at (3, 3), then draw line OA from the origin (O) to point A. A What is the equation of line OA? ② Mark point B on the circle at (2, 4), & draw line OB from the origin. C B What is the gradient of the line OB? 2 D How are the gradients of these graphs related? Perpendicular tangent What is the gradient of a line perpendicular to OB? Plot & label line CD - the line that is perpendicular to OB & passes through B. Draw & label the line that is parallel to CD & touches the circle at one point. Where on the circle will a tangent have a gradient of 2? ③ Sketch the line OD. D (4, − 2) (− 4, 2) Find the equation of the tangent at (6, − 2) ④ Find the gradient of this radius, is it positive or negative? . − 5 Find the equation of the tangent at (− 2, 6) Where do these tangents meet? (10, 10)

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk