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.

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- Nov 12th 2008, 08:36 AMalicequadratic 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. - Nov 12th 2008, 09:02 AMmasters
I think you probably meant to say: Show that $\displaystyle (x+8)^2=x^2+(x+5)^2$

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

$\displaystyle x^2-6x-39=0$

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