Geometry Questions

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

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

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?

$△ABC$ 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 ΔPQR, ∠Q=90
∘
. PQ=8 cm and PR=17 cm. If the bisector of ∠P meets QR at S, then what is the length (in cm) of SR?

In ΔABC, AB=20 cm, BC=7 cm and AC=15 cm. Side BC is produced to D such that ΔDAB∼ΔDCA. The length of CD is:

A student wants to know the area of a rhombus, one of whose diagonals is 6 cm. He measures another diagonal as 8 cm. What is the area of the rhombus?

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

Find the ratio of the curved surface area to the total surface area of a cylinder with diameter of base 14 cm and height 10 cm.

Given that triangle ABC is congruent to triangle DEF. If AC=11 m, ED=6 m, EF=15 m, ∠FDE=85
∘
and ∠ABC=55
∘
, then the perimeter of triangle ABC and ∠EFD are, respectively:

In a circle with centre 'O', if the angle subtended by an arc at the circumference ∠BCA=50
∘
, then what is the value of ∠BDA where D is another point on the same major arc segment?

In $\Delta ABC$, $AD$ is the bisector of $\angle A$ and intersects $BC$ at $D$. If $BC=a$, $AC=b$ and $AB=c$, then $BD$ is equal to:

In $\Delta ABC$, $BD\perp AC$ at $D$. $E$ is a point on $BC$ such that $\angle BEA=x^{\circ }$. If $\angle EAC=36^{\circ }$ and $\angle EBD=40^{\circ }$, then the value of $x$ is:

In ΔABC, P and Q are the middle points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR:RQ=1:4. If PR=5 cm, then BC= ?

Let A,B,C be the mid-points of sides XY,YZ and XZ, respectively of ΔXYZ. If the area of ΔXYZ is 8464 cm
2
, then find the area (in cm
2
) of ΔABC.

In ΔABC, AB and AC are produced to points D and E, respectively. If the bisectors of ∠CBD and ∠BCE meet at point O such that ∠BOC=76
∘
, then ∠A= ?

In ΔABC, D and E are points on sides AB and BC, respectively, such that DE∥AC. If BD=4 cm and AB=12 cm, then the ratio of the area of ΔBDE to that of quadrilateral ACED is:

A sector is cut from a circle of diameter $42\text{ cm}$. If the angle of the sector is $150^{\circ }$, then what is its area in ${\text{cm}}^2$? (Take $\pi =\frac{22}{7}$)

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: