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 : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.

Option 1: 18 cm

Option 2: 16 cm

Option 3: 20 cm

Option 4: 22 cm

Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:

Option 1: 12 cm

Option 2: 18 cm

Option 3: 4 cm

Option 4: 6 cm

Question : In a triangle ${ABC}, {AB}={AC}$ and the perimeter of $\triangle {ABC}$ is $8(2+\sqrt{2}) $ cm. If the length of ${BC}$ is $\sqrt{2}$ times the length of ${AB}$, then find the area of $\triangle {ABC}$.

Option 1: $32 \ cm^2$

Option 2: $28 \ cm^2$

Option 3: $16 \ cm^2$

Option 4: $36 \ cm^2$

Question : Triangle ABC and DEF are similar. If AB = 92 cm, BC = 48 cm, AC =120 cm, and the length of the smallest side of triangle DEF is 200 cm, then find the length of the longest side of triangle DEF.

Option 1: 400 cm

Option 2: 225 cm

Option 3: 350 cm

Option 4: 500 cm