Five mark example problem II — task. Mathematics State Board, Class 10.

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The line joining the points \(A(0,5)\) and \(B(4,1)\) is a tangent to a circle whose centre \(C\) is at the point \((4,4)\). Find

(i) the equation of the line \(AB\).

(ii) the equation of the line through \(C\) which is perpendicular to the line \(AB\).

(iii) the coordinates of the point of contact of tangent line \(AB\) with the circle.

Answer:

(i) The equation of the line \(AB\) is .

(ii) The equation of the line through \(C\) which is perpendicular to the line \(AB\) is .

(iii) The coordinates of the point of contact of tangent line \(AB\) with the circle is

(\frac{i}{i}, \frac{i}{i})

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15. Five mark example problem II