The line l is a tangent to the circle x^2 + y^2 = 40 at the point A. A is the point (2, 6). The line l crosses the x-axis at the point P. Work out the area of triangle OAP.

The area of OAP is 60. The missing information I need is to find the x coordinate of point P. To do this I need to find the equation of the tangent. For this I first found the equation of the radius by finding its gradient by dy/dx (6/2) which was 3. The tangent is perpendicular to radius therefore the product of the gradient of the tangent and the gradient of the radius must have a product of -1 making the gradient of the tangent -1/3. I then used the equation y1-y2 = m(x1-x2) to find the equation of the tangent which I got as y = -1/3x + 20/3. Then using this I could find the x coordinate of P as 20. Then I found the area of the triangle by using 1/2 x base x height so 1/2 x 20 x 6 gives me the answer of 60.