Triangle ABC is inscribed in a circle as shown above. What is the radi

Question

https://gmatclub.com/forum/download/file.php?id=48874 Triangle ABC is inscribed in a circle as shown above. What is the radius of the circle? (1) AB is a diameter of the circle. (2) AC = 3 and BC = 4. 2019-07-11_1223.png

Kinshook · Answer

S1:
AB is diameter of the circle 
No value of AB is provided
NOT SUFFICIENT

S2:
AC=3 and BC=4
No information is provided for AB.
NOT SUFFICIENT

S1&S2:
Since AB is diameter of the circle, AB will form right angle on a point on the circumference (C)
 => AB^2 = AC^2 + BC^2 
 => AB ^2 = 3^2 + 4^2 
=> AB = 5 since AB=-5 is not feasible.
 Radius = \frac{Diameter}{2}= \frac{5}{2} =2.5 
SUFFICIENT

IMO C

vishalkazone · Answer

Answer C

Option 1: No dimention is given so cannot calculate radius.
Not sufficient.

Option 2: Dimensions given but not sure about angle C to calculate radius.
Not Sufficient.

Combination:

Dimensions given and if AB is diameter then angle C is 90degree we can calculate radius.( No point doing calculation)

Sufficient.
Answer C

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Triangle ABC is inscribed in a circle as shown above. What is the radi

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