Question

$△$ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. Then find the value of $AC\times DC$.

Answer 1

Consider $\Delta$ABC and $\Delta$BDC,

$\angle$ABC = $\angle$BDC = ${90}^{\circ }$

$\angle$C = $\angle$C [Common angle]

Therefore by AA similarity criterion, $△$ABC and $△$BDC are similar. $\left[1mark\right]$

$\frac{AC}{BC}$ = $\frac{BC}{DC}$

$B{C}^2$ = $AC\times DC$ $\left[1mark\right]$