# Question Video: Relationships between Circles Mathematics

The radii of the two circles on the common center π are 3 cm and 4 cm. What is the length of line π΄π΅?

02:33

### Video Transcript

The radii of the two circles on the common centre π are three centimetres and four centimetres. What is the length of line π΄π΅?

Letβs add the information we know to the diagram. The centre of both circles is π, and this means the distance from π to any point on the outside of the smallest circle will be equal to three centimetres. It also means that the distance from π to any point on the outside of the largest circle will be equal to four centimetres. And so, the distance from π to π· is four centimetres. And the distance from πΆ to π· must be equal to one centimetre.

But the line weβre interested in is line π΄π΅. Thatβs this line. We noticed that the point π΄ falls on the outside of the smaller circle and point π΅ falls on the outside of the smaller circle. We can also see that the line π΄π΅ runs through the centre π. This means that the segment π΄π measures three centimetres and the segment ππ΅ measures three centimetres. We could say that line π΄π΅ is equal to line π΄π plus line ππ΅. Line π΄π measures three centimetres. Line ππ΅ measures three centimetres. Together, they form the measure of line π΄π΅. And so, we can say that line π΄π΅ is six centimetres long.

Letβs go back to that original sentence. Line π΄π΅ is equal to line π΄π plus line ππ΅. We know that the first segment is a radius of this circle, and the second segment is a radius of this circle. Line π΄π΅ is made up of two lines that run through the centre of the circle. And that means we can call line π΄π΅ a diameter of the circle. A diameter of the circle is always equal to two times the radius. And so, we can say the length of line π΄π΅ is six centimetres, and the diameter of the smaller circle with centre π is six centimetres.