Inscribed Triangle

[varungoel]

For the triangle shown above, where A, B and C are all points on a circle, and line segment AB has length 18, what is the area of triangle ABC?

(1) Angle ABC measures 30°.

(2) The circumference of the circle is 18(pi).

Can you please help explain the answer?

C
[spoiler]why isn't A sufficient by itself using the 30-60-90 rule[/spoiler]

[shankar.ashwin]

Using statement [A] alone I dont think you can decide if its a 30-60-90 triangle, for you cannot deduce that AB is the diameter from the statement, it could possibly be a chord thereby making the 30-60-90 conclusion invalid. Using [2] you can say that AB is the diameter and you need both to say its a 30-60-90 triangle thereby finding the area.

Hope you got it

For the triangle shown above, where A, B and C are all points on a circle, and line segment AB has length 18, what is the area of triangle ABC?

(1) Angle ABC measures 30°.

(2) The circumference of the circle is 18.

Can you please help explain the answer?

C
[spoiler]why isn't A sufficient by itself using the 30-60-90 rule[/spoiler]

[sl750]

From statement 1, we cannot conclude that the triangle is a right triangle. Because we are not told that the line AB=18 passes through the center of the circle

[1947]

Ans is E...bcos even with both A and B we do not know if the line is diameter and triangle is 30-60-90

please share OA

[varungoel]

The OA is C

Explanation: [spoiler]with statement 1, we dont know the other angles in the triangle so insufficient. with statement 2, we know 18 is the diameter, but we dont know the angles. together (hence C), we can calculate the area. [/spoiler]

[1947]

yes u r right....i missed PI.....Thanks