EASY

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The circumcentre of a right-angled triangle lies on .

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Important Questions on Coordinate Geometry

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

The sides of a triangle are

12 cm

35 cm

and

37 cm

. What is the circumradius of the triangle?

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Let the circumcentre of a triangle with vertices

A (a, 3), B (b, 5)

and

C (a, b), a b > 0

P (1, 1)

. If the line

A P

intersects the line

B C

at the point

Q (k_{1}, k_{2})

, then

k_{1} + k_{2}

is equal to

HARD

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Let

P

be a point inside a triangle

A B C

with

∠ A B C = 90 °

. Let

P_{1} and P_{2}

be the images of

P

under reflection in

A B

and

B C

respectively. The distance between the circumcentre of triangles

A B C

and

P_{1} P P_{2}

EASY

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

If the sides of a triangle are

3, 4

and

5

then the circumradius of the triangle is

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

The circumcentre of the triangle with vertices at

(- 2, 3), (1, - 2)

and

(2, 1)

HARD

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Let the straight lines

5 x - 3 y + 15 = 0

and

5 x + 3 y - 15 = 0

form a triangle with the

X

-axis. Then, the radius of the circle circumscribing this triangle is

HARD

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

The equations of the sides

A B, B C

and

C A

of a triangle

A B C

are

2 x + y = 0, x + p y = 39

and

x - y = 3

respectively and

P (2, 3)

is its circumcentre. Then which of the following is NOT true

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Let

A (α, - 2), B (α, 6)

and

C (\frac{α}{4}, - 2)

be vertices of a

∆ A B C

. If

(5, \frac{α}{4})

is the circumcentre of

∆ A B C

, then which of the following is NOT correct about

∆ A B C

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

The point

Q

is the image of the point

P (1, 5)

about the line

y = x

and

R

is the image of the point

Q

about the line

y = - x

. The circumcentre of the

Δ P Q R

EASY

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

In the given figure, $△ ABC$ is an isosceles triangle, in which $AB = AC, AD ⊥ BC, BC = 6 cm$ and $AD = 4 cm$ . The length of $AB$ is:

Question Image

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

A circle passes through the vertices of a triangle

A B C

. If the vertices are

A (- 2, 5), B (- 2, - 3)

, and

C (2, - 3)

then the centre of the circle is

HARD

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

The distance (in units) between the circumcentre and the centroid of the triangle formed by the vertices $(1, 2), (3, - 1)$ and $(4, 0),$ is

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

If angle

A

of triangle ABC is

30 °

and circum-radius of the triangle is

10 c m

, then what is the length of side

B C

EASY

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

The sides of triangle are

11 cm, 60 cm, 61 cm

.What is the radius of circle circumscribing the triangle?

EASY

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

An equilateral triangle of side

x

is inscribed in a circle of radius

y

. Which one of the following is correct?

HARD

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Let the equations of two sides of a triangle be

3 x - 2 y + 6 = 0

and

4 x + 5 y - 20 = 0 .

If the orthocenter of this triangle is at

(1, 1)

then the equation of it's third side is:

EASY

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Let

C (α, β)

be the circumcentre of the triangle formed by the lines

4 x + 3 y = 69

4 y - 3 x = 17

, and

x + 7 y = 61

. Then

(α - β)^{2} + α + β

is equal to

EASY

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Find the length of the altitude of an equilateral triangle with side

6 cm

. [Take

\sqrt{3} = 1.73

]

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

Let a triangle

A B C

be inscribed in a circle of radius

2

units. If the

3

bisectors of the angles

A, B

and

C

are extended to cut the circle at

A_{1}, B_{1}

and

C_{1}

respectively, then the value of

{[\frac{A A_{1} \cos \frac{A}{2} + B B_{1} \cos \frac{B}{2} + C C_{1} \cos \frac{C}{2}}{\sin A + \sin B + \sin C}]}^{2} =

EASY

Mathematics>Geometry>Coordinate Geometry>Special Points in a Triangle

R

is the circum radius of

Δ A B C

, then

A r e a (Δ A B C)

= ….

The circumcentre of a right-angled triangle lies on .

Important Questions on Coordinate Geometry

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