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The figure below consists of a square and an equilateral triangle connected together with a common side.

What is the measure of $x$ ?

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Important Questions on Triangles

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Mathematics>Geometry>Triangles>Properties of a Triangle

The equation of the base of an equilateral triangle is

x + y - 2 = 0

. If one of its vertex is

(2, - 1)

, then area of the triangle is

EASY

Mathematics>Geometry>Triangles>Properties of a Triangle

A B C

is an equilateral triangle.

P, Q

and

R

are the midpoints of sides

A B, B C

and

C A

respectively. If the length of the side of the triangle

A B C

8 c m

, then the area of

∆ P Q R

is:

HARD

Mathematics>Geometry>Triangles>Properties of a Triangle

In an equilateral

△ A B C

, side

B C

is produced to

D

and

D F ⊥ A B

such that

D F

is intersecting

A C

E

. If

B C = 2 C D

and

A F = 6 cm

, then the length (in

cm

) of

BF

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Mathematics>Geometry>Triangles>Properties of a Triangle

If the centroid of the triangle formed by points

(a, b), (b, c), (c, a)

is at the origin, then

a^{3} + b^{3} + c^{3}

is equal to

EASY

Mathematics>Geometry>Triangles>Properties of a Triangle

The area of an equilateral triangle is

18 \sqrt{3}

sq. units. Find the value of the side (in units) of the triangle.

EASY

Mathematics>Geometry>Triangles>Properties of a Triangle

An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. What is

∠ B D C

equal to?

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Mathematics>Geometry>Triangles>Properties of a Triangle

Δ A B C

is an equilateral triangle in which D, E and F are the points on side

B C, A C

and

A B

, respectively, such that

A D ⊥ B C, B E ⊥ A C

and

C F ⊥ A B

, which of the following is true?

EASY

Mathematics>Geometry>Triangles>Properties of a Triangle

∆ A B C

is an equilateral triangle and

A D ⊥ B C

, where

D

lies on

B C

. If

A D = 4 \sqrt{3} c m

, then what is perimeter (in cm)

MEDIUM

Mathematics>Geometry>Triangles>Properties of a Triangle

In an equilateral triangle

A B C, D, E, F

are the mid-points of

A B, B C,

and

A C

respectively. The quadrilateral

B E F D

is a _____.

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Mathematics>Geometry>Triangles>Properties of a Triangle

Let

l > 0

be a real number,

C

denote a circle with circumference $l$ and

T

denote a triangle with perimeter

l

. Then

HARD

Mathematics>Geometry>Triangles>Properties of a Triangle

Let

A B C D

be a trapezium with parallel sides

A B

and

C D

such that the circle

S

with

A B

as its diameter touches

C D

. Further, the circle

S

passes through the mid-points of the diagonals

A C

and

B D

of the trapezium. The smallest angle of the trapezium is

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Mathematics>Geometry>Triangles>Properties of a Triangle

Circles $C_{1}$ and $C_{2},$ of radii $r$ and $R$ respectively, touch each other as shown in the figure. The line $l$ which is parallel to the line joining the centres of $C_{1}$ and $C_{2},$ is tangent to $C_{1}$ at $P$ and intersects $C_{2}$ at $A, B$ . If $R^{2} = 2 r^{2},$ then $∠ A O B$ equals-

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