Question

In $△ABC$ , B is the right angle and BD is perpendicular to AC, then:

• A. ${BC}^2=AC\times DC$
• B. ${BC}^2=AD\times AC$
• C. ${BC}^2=BD\times AC$
• D. ${BC}^2={DC}^2+{AD}^2$

Answer 1

The correct option is A

${BC}^2=AC\times DC$

In $△ABCand△BDC$
$\angle ABC=\angle BDC={90}^{\circ }$
$\angle C=\angle C$ (common angle)

Therefore, $△ABC\sim △BDC$ [by AA similarity]
$\frac{BC}{DC}=\frac{AC}{BC}$
${BC}^2=AC\times DC$