Question

In $△ABC,AB=3cm,AC=4cm$ and AD is the bisector of $\angle$A. Find $BD:DC$.

[2 Marks]

Answer 1

In <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $△$ ABC, AD bisects <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∠BAC.

Angle Bisector Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle. [1 Mark]

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{BD}{DC}$ = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{AB}{AC}$ = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{3}{4}$

Hence, $BD:DC$ = $3:4$ [1 Mark]