If a triangle is inscribed in a circle such that a length of a side of

I solved this question again to understand the concept better.

Method:
One side = 3

We just know that one side of this triangle is 3 and it can be any side.

1) Two sides are equal and thus any two sides of this triangle can be equal but which two sides ?

Not sufficient to conclude anything.

BCE

2) 2*pi*r= 3*pi
r= 1.5

Diameter= 3

We already one side of the triangle is 3 and according to second statement diameter is 3. As we know diameter is the longest side of the triangle and thus no other side will equal 3. We can conclude that it is a right angled triangle.


B

Hi Bunuel,

Could please help me with this question.

Stmnt 1 is insufficient

From stmnt 2 we can find the diameter of the circle. But who said that one side of the triangle is on the diameter?

you can't have a side of 3 cm of an inscribed triangle that does not coincide with the diameter of the circle, which is also 3 cm.

The longest side an inscribed triangle can have is the diameter of the circle.

[quote="Leo8"][quote="Mehemmed"]Hi Bunuel,

very good question. thanks

Could someone please tell me if my logic for Statement (1) being insufficient is correct:


(1) the triangle could be right angled, but it also may not be. For example, we could have a triangle with length of 3 units and its an equilateral triangle with all sides equal to 3 units (which is isosceles), this is NOT a RAT. But on the other hand, we could have an isosceles right angled triangle (a 45-45-90 RAT) where the side lengths are 3 units and the other length (hyp) is 3root(2) units long.

Since we are unsure of which we have, (1) is INSUFFICIENT.

(2) tells us that the circle has a circumference of 3pi. This means that the diameter is 3 units. We are told in the q that the triangle that is inscribed in the circle has one side equal to three units. There is a property that states that if you have a triangle inscribed in a circle, and one of its sides is equal to the diameter of that circle, then the triangle has to be a RAT. Hence, (2) alone is sufficient to answer this question because (2) automatically tells us that the inscribed triangle is a RAT as one of its sides = diameter of circle.

Answer is B