### Video Transcript

Complete the following. If segment π΄π΅ is a chord in a circle with centre π, then the triangle π΄ππ΅ 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 π. Weβre told that the segment π΄π΅ 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 letβs look at our chord π΄π΅. And we can note that thereβs a triangle π΄ππ΅ created. Thatβs a triangle formed from the centre point π, with one line to π΄ and one line to π΅.

We donβt know the exact positioning of π΄ and π΅. 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 π΄π and ππ΅. Since we know that the line from π to π΄ 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 π΄ or π΅ will be, the lengths π΄π and ππ΅ 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 π΄ππ΅ is isosceles.