Find, without differentiation, the equation of the straight lines which pass through the point and are tangential to the circle,
Sorry what I did was...
Let the unknown point of intersection be
Length from circle center to
Since radius=2, the length of the line by pythagoras theorem
then, gradient of the radius from circle center to point of intersection
With the value of x found, i can find y but the equation of the line i got is different from the answer
After defining one of the tangency triangles you need to find the altitude on the hypothenuse and the segments it creats on the hypot.A slope of the tangent will then be definable.Next use point slope formula to find the lines.
Another way to do this, without (directly) calculating the gradient, is to note that, since the distance from the point of tangency to (4, 0) is , we have, for that angle, C, sin(C)= 2/5 and . It follows from that that cos(A)= 2/5 and .
From those, we can calculate that the coordinates of point B are and then we can find the equation of the line using the "two point" formula.
In geometry the slope of a line = rise /run so strictly speaking the tangent at C is not the slope but is the same quantity as can be seen when you erect the altitude on hypot of ABC. I admit that geometry today would allow your solution but would be interested in a few replies.