Question

Start with `DeltaOAU`, with `bar(OA) = a` , extend `bar(OU)` in such a way that `bar(UB) = b`, with `B` on `bar(OU)`. Construct a parallel line to `bar(UA)` intersecting `bar(OA)` at C. Show that, `bar(AC) = ab`?

Answer 1

see explanation.

Explanation:

Draw a line `UD`, parallel to `AC`, as shown in the figure.
`=> UD=AC`
`DeltaOAU and DeltaUDB` are similar,
`=> (UD)/(UB)=(OA)/(OU)`
`=> (UD)/b=a/1`
`=> UD=ab`
`=> AC=ab " (proved)"`