Question : In $\triangle $ABC, AD$\perp$ BC and AD² = BD × DC. The measure of $\angle$ BAC is:

Option 1: 60°

Option 2: 75°

Option 3: 90°

Option 4: 45°

Question : In $\triangle ABC$, $\angle B=60°$, $\angle C=40°$. AD is the bisector of $\angle A$ and AE is drawn perpendicular on BC from A. Then the measure of $\angle EAD$ is:

Option 1: $40^{\circ}$

Option 2: $30^{\circ}$

Option 3: $10^{\circ}$

Option 4: $80^{\circ}$

Question : $ABC$ is an isosceles triangle with $AB = AC$, The side $BA$ is produced to $D$ such that $AB = AD$. If $\angle ABC = 30^{\circ}$, then $\angle BCD$ is equal to:

Option 1: $45^{\circ}$

Option 2: $90^{\circ}$

Option 3: $30^{\circ}$

Option 4: $60^{\circ}$

Question : In $\triangle$ABC, $\angle$A = $\angle$B = 60°, AC = $\sqrt{13}$ cm, the lines AD and BD intersect at D with $\angle$D = 90°. If DB = 2 cm, then the length of AD is:

Option 1: 3 cm

Option 2: 3.5 cm

Option 3: 4 cm

Option 4: 4.7 cm

Question : $\angle A$ of $\triangle ABC$ is a right angle. $AD$ is perpendicular on $BC$. If $BC= 14$ cm and $BD= 5$ cm, then measure of $AD$ is:

Option 1: $2\sqrt5$ cm

Option 2: $\sqrt5$ cm

Option 3: $3\sqrt5$ cm

Option 4: $3.5\sqrt5$ cm