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GMAT - Data Sufficiency - Geometry

If arc PQR above is a semicircle, what is the length of diameter PR

If arc PQR above is a semicircle, what is the length of diameter PR?

(1) a=4
(2) b=1

In triangle PQR, angle Q = 900 (Angle subtended by the diameter at the circumference)

Using pythagorus theorem in all three triangles

PQ2 + QR2 = PR2 .. (i)

PQ2 = a2 + 22 = a2 + 4 ... (ii)

QR2 = b2 + 22 = b2 + 4 ... (iii)

replacing PQ and QR in equation 1, and replacing PR = a + b

a2 + 4 + b2 + 4 = (a + b)2

a2 + b2 + 8 = a2 + b2 + 2ab

ab = 4 ... (iv)

Statement 1:

a = 4

from (iv)

b = 4/a = 4/4 = 1

diameter = a+b = 1 + 4 = 5

sufficient

Statement 2:

b = 1

from (iv)

a = 4/b = 4/1 = 4

diameter = a+b = 4 + 1 = 5

sufficient