Triangles Questions

The sides of a right-angled triangle, right-angled at B, are 6, 8 and 10 units. C is the vertex opposite to the side with length 8 units. What is the value of tan
2
A+cos
2
C?

△PQR and △ABC are two congruent triangles. If the area of △PQR is 225cm
2
, then the area of △ABC is:

If three angles of a triangle are (18x+6
∘
), (10x+30
∘
) and (15x+15
∘
), then the triangle is:

$△ABC$ and $△ABD$ are on a common base $AB$, with $AC=BD$ and $BC=AD$. Which of the following options is true?

In $△OPQ$, $\angle O=50^{\circ }$, $\angle P=70^{\circ }$, and the bisectors of $\angle P$ and $\angle Q$ meet at $R$. Find $\angle PRQ$.

In an isosceles △LMN, LM=LN, and ∠MLN=37
∘
. Find ∠MNL.

In △ABC, D is the mid-point of BC and G is the centroid. If GD = 10 cm, then the length of AD is ____________.

In a triangle ABC, P is the midpoint of BC. If AB = (2x+4) cm, AC = 6 cm and AP ⊥ BC, then the value of x is: