PQ is a diameter of a circle and AB is a perpendicular chord cutting it at N. Prove that PN is equal in length to the perpendicular from P on to the tangent at A.
I have attached a diagram of how i imagine this situation to look. If my diagram is correct and I'm supposed to be proving that the two yellow segments are equal, then I'm not sure how to prove this.
However, if my diagram is wrong could someone please correct it so i can visulaise the situation.
September 23rd 2010, 07:53 AM
What you have drawn is a perpendicular from the tangent to PQ. But what is required is a perpendicular from PQ to the tangent. Suppose it intersects the tangent at X, then angle PXA will be 90 degrees. In your diagram, if you draw it, a part of it will be inside the circle.
September 23rd 2010, 08:10 AM
As the chord moves to the right, the tangent would meet the perpendicular to P in your drawing to nearly infinity, which does not agree with the proof.
I think this is how the drawing is meant to rather be: