Answer:
Let the chord- part of VC inside smaller circle be a, and same of CU be b.
According to intersecting secants theorem we have:
- CI * (CI + a) = CJ * (CJ + b)
and
- VC *(CI + a) = CU * (CJ + b)
From the second equation we get:
- CU = VC * (CI + a) / (CJ + b)
From the first equation we get:
- CI + a = CJ * (CJ + b) / CI,
substitute this into the second equation:
- CU = VC * CJ * (CJ + b) / CI * 1/ (CJ + b)
- CU = VC * CJ / CI
- CU * CI = VC * CJ
Proved
