In △ABC, BD ⟂ AC at D and ∠DBC = 71°. E is a point on BC such that ∠CAE = 55°. What is the measure of ∠AEB?

In triangle PQR, the sides PQ and PR are fixed with lengths 26 cm and 17 cm, respectively. Point S lies on side QR such that the ratio QS:SR = 3:5. The area of triangle PQS is 120 cm². Find the area of triangle PQR.

The midpoints of a triangle with sides 16 cm, 24 cm, and 32 cm are joined. Find the area (in cm²) of the triangle formed by these midpoints.

In an isosceles triangle △ABC, AB = AC. Each of the equal angles is 5° more than three-fourths of the third angle. Find the value of (3∠A − ∠B).

In Δ ABC, D, E and F are the mid-points of sides AB, BC and CA, respectively. Four triangles, Δ ADF, Δ BDE, Δ CEF and Δ DEF are formed by using A, B, C, D, E and F. The following observations are made about these four triangles.

i. All the four triangles have equal perimeter.

ii. All the four triangles have equal area.

Which of the following is true regarding the given observations?

X and Y are the midpoints of sides AB and AC, respectively, of triangle ABC. If BC = 9 cm, AB = 11 cm and AC = 14 cm, then what is the ratio of the perimeters of trapezium XBCY to triangle ABC to triangle AXY?

In triangle ABC and PQR, \(AB = AC\), \(\angle C = \angle P\) and \(\angle B = \angle Q\). Then both the triangles are:

ABC is a right-angled triangle in which angle A is a right angle. Which side needs to be bisected to construct two other right-angled triangles?

Triangle ABC is similar to triangle PQR. If AB = 5 cm and PQ = 3 cm, then state the value of \(\frac{\text{ar}(\Delta ABC)}{\text{ar}(\Delta PQR)}\):

In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:

The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is

In ∆ABC, 2∠A = 3∠B = 6∠C. What is the value of the largest angle among these three angles?

The longest side in a right-angled triangle is called :