ABT is a secant of a circle which intersects the circle at A and B and PT is a tangent to the circle at P. If PT=5cms, BT=2.5cms Find AB.

Question

This is a question from theoritical geometry. Need answer with drawing.

Answer 1

"This is a question from theoritical geometry. Need answer with drawing."

 

Is this a theocratic question, or a theoretical question?

 

I think I have the picture. Secant ABT starts at point A on circle O, intersects circle at B, and continues on to external point T.

Then from T there's a tangent to the circle, P being the pont of tangency.

 

The operative theorem here is that es = t², where e is the external length BT = 2.5 and s = entire secant's length, AT, and t is the length of the tangent (t = PT = 5).

 

So 2.5(s) = 5² which leads to s = 10.  Therefore AB = s - e = 10 - 2.5 = 7.5 cm