Powerprep - triangle in a circle

Question

Could anyone please explain this?

querio · Answer

D

QR = d
PQ = c
point T is between points P and R.

Stmt 1:
If a triangle is inscribed in a circle and one of the sides of the triangle coincides with the diameter of the circle, then the triangle is a right triangle (important rule that allows you to apply the Pythagorean theorem to triangle PQR) . 
triangle PQR: (a+b)^2 = d^2 + c^2;
triangle PTQ: a^2+2^2=c^2;
triangle TQR: b^2+2^2=d^2

solving for these equations, you get b=1 --> Sufficient

Stmt 2:
idem above explanation, but in this case 'b' is known and you have to calculate 'a' ---> Sufficient

ggarr · Answer

I'm sorry. Will you explain where you went from here:
 
I'm doing something wrong.

goalsnr · Answer

ggar hope this helps you :
Diameter d= a+b

(a+b)^2 = (PQ)^2+(QR)^2
(PQ)^2 = a^2+4 ...(1)
(QR)^2 = b^2+4....(2)
Subst (1) and (2)
(a+b)^2 = a^2+4+b^2+4 

now if a is given we can find b and hence d
similarly if b is given we can find a and hence d

 so Stat 1 is suff and stat 2 is suff, Hence D

ggarr · Answer

oh wow, I completely forgot that a and b were given to us and that all I needed to do was replace a and b w/each ones respective equivalents.

Thanks goalsnr!!

Powerprep - triangle in a circle

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