Thread: question on properties of circle 9

Referring to the attached pic, find the radii of both circles.

Hello ukorov

Originally Posted by ukorov

Referring to the attached pic, find the radii of both circles.

In the attached diagram, I have marked the points of contact with the smaller circle as E and F.

Then, if the radius of the smaller circle is

and if , then (tangents from a point to a circle are equal)



In cm (Pythagoras)



Solving these simultaneous equations: .

So the radius of the smaller circle is cm.

Similarly let and

Express the lengths of and in terms of and . Then use the fact that to form another equation. Solve these equations to find , the radius of the larger circle.

Grandad

Originally Posted by Grandad

Hello ukorovIn the attached diagram, I have marked the points of contact with the smaller circle as E and F.

Then, if the radius of the smaller circle is [/size]

and if , then (tangents from a point to a circle are equal)



In cm (Pythagoras)



Solving these simultaneous equations: .

So the radius of the smaller circle is cm.

Similarly let and

Express the lengths of and in terms of and . Then use the fact that to form another equation. Solve these equations to find , the radius of the larger circle.

Grandad

PQ = 6 = w + z
w = 6 - z .....(1)
TA = TP + w = 10 + w
TB = TQ + z = 8 + z
hence 10 + w = 8 + z .....(2)
(1) to (2):
10 + 6 - z - 8 = z
2z = 8
z = 4
hence larger circle has radius 4cm.

Thanks