# Math Help - quadratic equations?

1. ## quadratic equations?

AT is a tangent at T to a circle, centre O.
OT = x cm AT = (x+5) cm OA = (x+8) cm
a) Show that x^2-6x-39=0
b) Solve the equation x^2-6x-39=0 to find the radius of the circle

Give your answer correct to 3 significant figures.

Someone please help.

2. Originally Posted by alice
AT is a tangent at T to a circle, centre O.
OT = x cm AT = (x+5) cm OA = (x+8) cm
a) Show that x^2-6x-39=0
I think you probably meant to say: Show that $(x+8)^2=x^2+(x+5)^2$

$x^2+16x+64=x^2+x^2+10x-25$

$x^2-6x-39=0$
Originally Posted by alice
b) Solve the equation x^2-6x-39=0 to find the radius of the circle

Give your answer correct to 3 significant figures.
The quadratic will not factor, so use the quadratic formula to solve. Use only the positive root and round to 3 sig digits.

I got $x=\frac{6+\sqrt{192}}{2}\approx 9.93$