# 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?

Apr 23, 2018

see explanation.

#### Explanation:

Draw a line $U D$, parallel to $A C$, as shown in the figure.
$\implies U D = A C$
$\Delta O A U \mathmr{and} \Delta U D B$ are similar,
$\implies \frac{U D}{U B} = \frac{O A}{O U}$
$\implies \frac{U D}{b} = \frac{a}{1}$
$\implies U D = a b$
$\implies A C = a b \text{ (proved)}$