Question

ab and CD are common tangent to two circles of equal radii prove that AB=CD

Answer 1

Answer:

Step-by-step explanation:

Since AB and CD are common tangent to two circles of equal radii, our aim is to prove that AB = CD.

Then, by the picture bellow, we can say that OA = OD = PC = BP, which are equal to the radius of the circles.

Then if we sum them in pairs we get OA + OD = PC + PB ⇔ AD = BC.

AD and BC are the diameters of the circles.

Then we can compare the angles and conclude that AB = CD.

Hence proved