Let ABCD be a rectangle with AB = 72 cm and BC = 30 cm. A circle passing through points A and C cuts the side AB at P such that AP = 56 cm. The radius, in cm, of the circle is
Question and options
Let ABCD be a rectangle with AB = 72 cm and BC = 30 cm. A circle passing through points A and C cuts the side AB at P such that AP = 56 cm. The radius, in cm, of the circle is
Answer and explanation
Correct answer: A - \(\frac{221}{5}\)
Take A(0,0), P(56,0), C(72,30). Centre lies on x = 28; with centre (28,k): 28^2 + k^2 = 44^2 + (30-k)^2 gives 60k = 2052, k = 34.2. r^2 = 784 + 1169.64 = 1953.64, r = 44.2 = 221/5.
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