Triangles Set-1

Q1. In right triangle ABC right-angled at C, the altitude from C meets hypotenuse AB at D. If AD = 4 and DB = 9, find the length of CD.

Q2. In triangle ABC, the sides are $AB=13$, $AC=15$, $BC=14$. A median from vertex A meets $BC$ at M. The length $AM$ equals:

Q3. In triangle ABC, $AB=17,\ AC=15,\ BC=8$. Let D be the foot of the perpendicular from C to AB. Find the lengths $AD$ and $DB$. (Give exact values.)

Q4. In triangle ABC, AB = 10 and AC = 14. Point D lies on BC such that AD is perpendicular to BC and divides BC in the ratio $BD:DC=4:5$. The length of BC is:

Q5. In triangle ABC, BC=6,\ AB=10,\ AC=8. Point D lies on BC with $BD=2$ and $DC=4$. The length $AD$ is:

Q6. In triangle ABC, sides AB = 6, AC = 8 and BC = 10. A perpendicular is drawn from A to BC meeting BC at D. The length of AD is:

Q7. In triangle ABC, side BC = 14, CA = 15 and AB = 13. The length of the median from A to BC is:

Q8. In triangle ABC, DE is drawn parallel to BC with D on AB and E on AC. If $AD=3,\ DB=6,\ AE=4$, then the length $EC$ is:

Q9. Sides of triangle ABC are $13,\;14,\;15$. The circumradius $R$ of the triangle equals:

Q10. In triangle ABC, $AB=13,\ BC=14,\ CA=15$. Point $D$ on $BC$ satisfies $BD=4,\ DC=10$. The length $AD$ equals:

Q11. In triangle ABC the lengths of the sides are $13,\;14,\;15$. What is the area of triangle ABC?

Q12. In triangle ABC, a line through points D on AB and E on AC is drawn parallel to BC. If the area of $\triangle ABC$ is $200$ and the area of $\triangle ADE$ is $72$, what is $\dfrac{AD}{AB}$?

Q13. In right triangle ABC, $\angle B=90^\circ$. The altitude from B meets hypotenuse AC at H and divides AC into segments $AH=9$ and $HC=16$. The lengths of AB and BC are respectively:

Q14. In triangle ABC, $AB=13,\;AC=15,\;BC=14$. Let AD be the internal bisector of $\angle A$ meeting BC at D. The length of AD equals:

Q15. A triangle has side lengths $7,\;8,\;9$. The radius $r$ of its incircle is: