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 : $ABC$ is a right-angled triangle with $\angle BAC=90°$ and $\angle ACB=60°$. What is the ratio of the circumradius of the triangle to the side $AB\ ?$

Option 1: $1:2$

Option 2: $1:\sqrt3$

Option 3: $2:\sqrt3$

Option 4: $2:3$

Question : In triangle ABC, $\angle$ B = 90°, and $\angle$C = 45°. If AC = $2 \sqrt{2}$ cm then the length of BC is:

Option 1: 3 cm

Option 2: 2 cm

Option 3: 1 cm

Option 4: 4 cm

Question : If it is given that for two right-angled triangles $\triangle$ABC and $\triangle$DFE, $\angle$A = 25°, $\angle$E = 25°, $\angle$B = $\angle$F = 90°, and AC = ED, then which one of the following is TRUE?

Option 1: $\triangle \mathrm{ABC} \cong \triangle \mathrm{FED}$

Option 2: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DFE}$

Option 3: $\triangle \mathrm{ABC} \cong \triangle \mathrm{EFD}$

Option 4: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DEF}$

Question : A circle of radius 4 cm is drawn in a right-angle triangle ABC, right-angled at C. If AC = 12 cm, then the value of CB is:

Option 1: 8 cm

Option 2: 12 cm

Option 3: 20 cm

Option 4: 16 cm