Question

In the given figure, AB > AC. Then which of the following is true?
(a) AB < AD
(b) AB = AD
(c) AB > AD
(d) Cannot be determined

Answer 1

(c) AB > AD

$AB>AC$ is given.

∴ $\angle ACB>\angle ABC$

$$\begin{gathered} \mathrm{Now},\angle ADB>\angle ACD(\mathrm{exterior}\mathrm{angle}) \\ \Rightarrow \angle ADB>\angle ACB>\angle ABC \\ \Rightarrow \angle ADB>\angle ABD\Rightarrow AB>AD \end{gathered}$$