Question

I need help with 23-25, you can only explain one, I think I might be able to do the rest.

Answer 1

From the given figure, we can see the AB and CD are perpendicular to each other. Let the point of intersection of AB and CD be O as shown in the attached image.

Join AC and BC

Consider the triangle COA,

By Pythagoras theorem, which states

`(Hypotenuse)^(2)=(Base)^(2)+(Perpendicular)^(2)`

`(AC)^(2)=(CO)^(2)+(OA)^(2)` (Equation 1)

CO=OD= 3 in (If two congruent circles intersect at two points, then their centers lie on the perpendicular bisector of the common chord)

AO=OB=4 in

From equation 1, we get

`(AC)^(2)=(3)^(2)+(4)^(2)`

`(AC)^(2)=25`

`AC= √(25)= 5` in.