Question : Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact and $\angle$PAB = 40°. The measure of $\angle$ABP is:

Option 1: 45$^\circ$

Option 2: 55$^\circ$

Option 3: 50$^\circ$

Option 4: 40$^\circ$

Question : In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65° and the bisector of $\angle$BAC meets BC in D. Then $\angle$ADB is:

Option 1: 40°

Option 2: 75°

Option 3: 90°

Option 4: 105°

Question : If two circles of radii 18 cm and 8 cm touch externally, then the length of a direct common tangent is:

Option 1: 24 cm

Option 2: 14 cm

Option 3: 16 cm

Option 4: 12 cm

Question : ABC is an isosceles triangle such that AB = AC, $\angle$ABC = 55°, and AD is the median to the base BC. Find the measure of $\angle$BAD.

Option 1: 50°

Option 2: 55°

Option 3: 35°

Option 4: 90°

Question : If the angle of a right-angled triangle is 35°, then find the other angles.

Option 1: 90° and 75°

Option 2: 90° and 35°

Option 3: 90° and 55°

Option 4: 90° and 45°