Complete the following. If segment 𝐴𝐵 is a chord in a circle with centre 𝑀, then the triangle 𝐴𝑀𝐵 is what. Option A, an equilateral triangle option. Option B, a scalene triangle. Option C, an isosceles triangle.
So in this question, we have a circle with a centre 𝑀. We’re told that the segment 𝐴𝐵 is a chord in the circle. We can recall that the chord of a circle is a straight line whose end points lie on the circle. So we could draw our chord to look something like this. We can note that the special chord which passes through the centre of the circle would be the diameter. So let’s look at our chord 𝐴𝐵. And we can note that there’s a triangle 𝐴𝑀𝐵 created. That’s a triangle formed from the centre point 𝑀, with one line to 𝐴 and one line to 𝐵.
We don’t know the exact positioning of 𝐴 and 𝐵. For example, they could be almost opposite each other on the circle. Or they could be very close together on the outside of the circle. However, we do know one thing that will remain the same. And that is the length 𝐴𝑀 and 𝑀𝐵. Since we know that the line from 𝑀 to 𝐴 goes from the centre of the circle to the outside edge, then we can say that that length is equal to the radius of the circle. So no matter where 𝐴 or 𝐵 will be, the lengths 𝐴𝑀 and 𝑀𝐵 will always be the radius of the circle.
A triangle that has two sides of equal length will be an isosceles triangle. Therefore, we can say that triangle 𝐴𝑀𝐵 is isosceles.