In the figure, the circles are concentric with centre O. B is a point on the larger circle. D is a point on the smaller circle. BD is joined, provided that BD touches the circle at only one point. Now OB is joined and extended to meet the larger circle at A. Find the distance between points A and D if the radii of the circles are 4*sqrt(13) and 8 units respectively.

Guest Jan 4, 2021

#1**+2 **

Let O = (0, 0), D = (0, -8). Then B = (-12, -8) because OD = 8 and OB = 4sqrt(13), so by the Pythagorean Theorem, BD = 12

Then, since AB is a line segment passing through O, we have that A = (12, 8). Use the distance formula from (0, -8) to (12, 8) and get sqrt((12-0)^2+(8-(-8))^2) = sqrt(12^2+16^2) = 20, so AD = 20.

This is probably not the most efficient way, but We Still get the right answer.

JoLink Jan 4, 2021

#4**+1 **

Hello JoLink!!!

I think you might have copied CoolStuffYT's answer. Could you please not plagarize or take credit for other peoples answers?

It is very rude to other people and plagarizing is not cool.

Here is CoolStuffYT's answer: https://web2.0calc.com/questions/help_7500

DewdropDancer
Jan 4, 2021

#2**+1 **

We might also say that AB = 8 sqrt (13), and as OD=8, BD = sqrt(OB^2 - OD^2) = sqrt(208 - 64) = 12.

Extend BD to meet the circle at C. Then, BC = 2 BD = 24. Then, 832 -576 = 256, so AC = 16. Thus, AD = sqrt(AC^2 + DC^2) = sqrt(256+144) = sqrt(400) = 20.

Pangolin14 Jan 4, 2021

#5**0 **

Once again JoLink you have stolen another person's work.

This is a copy of CoolStuffYT's answer on July 20.

https://web2.0calc.com/questions/help_7500

You can present other people's work in the form of a link. You will be thanked for finding the answer. (Even if it is not stated)

**However:**

If you do not stop stealing other people's work you will be banned from this forum.

Melody Jan 4, 2021