Question : ABCD is a trapezium with AD and BC parallel sides and E is a point on BC. The ratio of the area of ABCD to that of AED is:

Option 1: $\mathrm{\frac{AD}{BC}}$

Option 2: $\mathrm{\frac{BE}{EC}}$

Option 3: $\mathrm{\frac{AD+BE}{AD+CE}}$

Option 4: $\mathrm{\frac{AD+BC}{AD }}$

Question : A triangle and a parallelogram have the same base 28 cm and the same area. If the height of the parallelogram is 12 cm, then find the length of the altitude of the triangle.

Option 1: 28 cm

Option 2: 23 cm

Option 3: 24 cm

Option 4: 21 cm

Question : ABCD is a quadrilateral. The length of the diagonal AC is 24 cm. The sum of the perpendicular drawn from vertex B and D on the diagonal AC is 10 cm. What is the area of the quadrilateral?

Option 1: 240 cm²

Option 2: 180 cm²

Option 3: 120 cm²

Option 4: 90 cm²

Question : A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, then the radius of the circle is:

Option 1: $2 \sqrt{3} {~cm}$

Option 2: $\sqrt{19} {~cm}$

Option 3: $\sqrt{17} {~cm}$

Option 4: $3 \sqrt{2} {~cm}$

Question : AB is a chord in a circle of radius 13 cm. From centre O, a perpendicular is drawn through AB intersecting AB at point C. The length of OC is 5 cm. What is the length of AB?

Option 1: 24 cm

Option 2: 12 cm

Option 3: 20 cm

Option 4: 15 cm