Proof of tangent - GCSE maths grade 8 ish

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This video deals with around a grade 8 ish, GCSE maths proof of tangent question. The whole idea is that it can be treated in a similar way to solving quadratic simultaneous equations, by substitution, but in this case there is only a single point.

Prove algebraically that the straight line with the equation x - 2y = 10 is a tangent to the circle with equation x² + y² = 20

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[kirstenlillie]

Hi Simon, I've just done this question using a different method, to get a geometric-algebraic proof, and I wondered if you would comment on its validity as an exam answer? I used the gradient of the tangent (0.5) to determine the gradient of the radius (-2) at the point where they meet. Using the geometry of a circle with centre (0, 0), the equation of the radius can be found: y = -2x, which meets x - 2y = 10 at the point (2, -4), which is also a point on the circle with the given equation. QED.

[hadyaq]

Hi simon! im wondering if you could go through the gcse maths edexcel specimen papers set 2 for foundation? I cant find anyone who has done it, and your the only person who explains well. Ive completed the non calc paper, so could you go over that first? thanks! :)

[jamilaaltaf]

do have anything on geometry of striaght lines and circles plz simon if u can

[tfueturner]

Hi Simon, I have a question about rearranging formula