Question : ABCD is a quadrilateral in which BD and AC are diagonals. Then, which of the following is true:

Option 1: AB + BC + CD + DA < (AC + BD)

Option 2: AB + BC + CD + DA > (AC + BD)

Option 3: AB + BC + CD + DA = (AC + BD)

Option 4: AB + BC + CD + DA > 2(AC + BD)

Question : $\triangle$ABC is similar to $\triangle$PQR and AB : PQ = 2 : 3. AD is the median to the side BC in $\triangle$ABC and PS is the median to the side QR in $\triangle$PQR. What is the value of $(\frac{BD}{QS})^2$?

Option 1: $\frac{3}{5}$

Option 2: $\frac{4}{9}$

Option 3: $\frac{2}{3}$

Option 4: $\frac{4}{7}$

Question : For congruent triangles $\triangle$ABC and $\triangle$DEF, which of the following statements is correct?

Option 1: Perimeter of $\triangle \mathrm{ABC}=\frac{1}{2}$ Perimeter of $\triangle \mathrm{DEF}$

Option 2: Perimeter of $\triangle \mathrm{ABC}=$ Perimeter of $\triangle \mathrm{DEF}$

Option 3: Perimeter of $\triangle \mathrm{ABC}<$ Perimeter of $\triangle \mathrm{DEF}$

Option 4: Perimeter of $\triangle \mathrm{ABC}>$ Perimeter of $\triangle \mathrm{DEF}$

Question : ABC is an isosceles triangle inscribed in a circle. If AB = AC = $12\sqrt{5}$ cm and BC = 24 cm, then the radius of circle is: 

Option 1: 10 cm

Option 2: 15 cm

Option 3: 12 cm

Option 4: 14 cm

Question : $O$ is the circumcentre of the isosceles $\triangle ABC$. Given that $AB = AC = 5$ cm and $BC = 6$ cm. The radius of the circle is:

Option 1: 3.015 cm

Option 2: 3.205 cm

Option 3: 3.025 cm

Option 4: 3.125 cm