Question : If $\frac{a^{2} - bc}{a^{2}+bc}+\frac{b^{2}-ca}{b^{2}+ca}+\frac{c^{2}-ab}{c^{2}+ab}=1$, then the value of $\frac{a^{2}}{a^{2}+bc}+\frac{b^{2}}{b^{2}+ac}+\frac{c^{2}}{c^{2}+ab}$ is:

Option 1: 0

Option 2: 1

Option 3: –1

Option 4: 2

Question : $\triangle ABC$ is an isosceles triangle with AB = AC = 15 cm and an altitude from A to BC of 12 cm. The length of side BC is:

Option 1: 9 cm

Option 2: 12 cm

Option 3: 18 cm

Option 4: 20 cm

Question : A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm, and AC = 24 cm, and sides AB, BC, and AC touch circle at D, E, and F, respectively. The measure of AD is:

Option 1: 10 cm

Option 2: 20 cm

Option 3: 6 cm

Option 4: 14 cm

Question : In a $\triangle$ABC, DE||BC, D and E lie on AB and AC, respectively. If AB = 7 cm and BD = 3 cm, then find BC : DE.

Option 1: 2 : 3

Option 2: 3 : 2

Option 3: 3.5 : 2

Option 4: 7 : 2

Question : In $\triangle$ABC, D and E are points on the sides BC and AB, respectively, such that $\angle$ACB = $\angle$ DEB. If AB = 12 cm, BE = 5 cm and BD : CD = 1 : 2, then BC is equal to:

Option 1: $8 \sqrt{3}$ cm

Option 2: $5 \sqrt{5}$ cm

Option 3: $6 \sqrt{5}$ cm

Option 4: $6 \sqrt{3}$ cm