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:

Question : ABC is an isosceles right-angle triangle. $\angle ABC = 90 ^{\circ}$ and AB = 12 cm. What is the ratio of the radius of the circle inscribed in it to the radius of the circle circumscribing $\triangle ABC$?

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:

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:

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 $\triangle {ABC}$.