In a △ X Y Z let x , y , z be the lengths of sides opposite to the angles X , Y , Z respectively and 2 s = x + y + z . If s - x 4 = s - y 3 = s - z 2 and area of incircle of the triangle △ X Y Z is 8 π 3 , then

The radius of circumcircle of the triangle △ X Y Z is 35 6 6

ln a △ A B C , A = 30 ° + C and R = ( 3 + 1 ) r , where r is the inradius and R is the circumradius, then

A B C is a right-angled triangle

∠ A = 75 ° , ∠ B = 60 ° , ∠ C = 45 °

EASY

Earn 100

Name the orthocentre of $△ P Q R$ .

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Important Questions on Properties of a Triangle

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

$X M$ is a median in $△ X Y Z, X Y^{2} + X Z^{2} = 328$ and $X M = 8$ then $Y Z =$ _____.

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

The sum of all the three sides of an equilateral triangle is

15 \sqrt{3} cm

. The height of the triangle is_____.

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

The length of side

A B

and side

B C

of a scalene triangle

A B C

are

12 cm

and

8 cm

respectively. The measure of angle

C

59 °

. Find the length of side

A C

HARD

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

In a

△ X Y Z

let

x, y, z

be the lengths of sides opposite to the angles

X, Y, Z

respectively and

2 s = x + y + z .

\frac{s - x}{4} = \frac{s - y}{3} = \frac{s - z}{2}

and area of incircle of the triangle

△ X Y Z

\frac{8 π}{3}

, then

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

In a Triangle , if

AB = AC

and

∠ ABC = 72 °

, then

∠ BAC

is:

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

Question Image

$P, Q$ and $R$ are the midpoints of the sides of the triangle $A B C$ . What type of quadrilateral is $P Q C R$ ?

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

∆ ABC

is an equilateral triangle with side

18 cm .

D is a point on BC such that BD

= \frac{1}{3} BC

. Then length (in cm) of A D is:

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

ln a

△ A B C

A = 30 ° + C

and

R = (\sqrt{3} + 1) r

, where

r

is the inradius and

R

is the circumradius, then

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

The perimeter of an isosceles triangle is

50 cm

. If the base is

18 cm

, then find the length of the equal sides.

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

In the given figure

△ ABC

, if

θ = 80 °,

the measure of each of the other two angles will be:
Question Image

HARD

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

Three circles of radii

1, 2

and

3

units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centres of the circles is

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

$ABC$ is an equilateral triangle of side $2 a$ , then length of one of its altitude is $a \sqrt{x}$ . The value of $a$ is _____.

HARD

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

Let

X Y

be the diameter of a semicircle with center

O .

Let

A

be a variable point on the semicircle and

B

another point on the semicircle such that

A B

is parallel to

X Y .

The value of

∠ B O Y

for which the inradius of triangle

A O B

is maximum, is

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

In a triangle

A B C

, the medians

A D

and

B E

intersect at

G

. A line

D F

is drawn parallel to

B E

such that

F

is on

A C

. If

A C = 9 cm

, then what is

C F

equal to?

HARD

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

If the lengths of the sides of a triangle are

15, 20, 25

units. Find the circumradius of the triangle.

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

Δ A B C

, if

a : b : c = 4 : 5 : 6

, then the ratio of the circumradius to its inradius is

MEDIUM

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

d_{1}, d_{2}, d_{3}

are the diameters of three ex-circles of a

Δ A B C

, then

d_{1} d_{2} + d_{2} d_{3} + d_{3} d_{1} =

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

What is the area of a triangle whose sides are

7 cm, 24 cm and 25 cm ?

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

The side of an equilateral triangle is

10 c m

. Find its area (in

c m^{2}

EASY

Mathematics>Geometry>Properties of a Triangle>Medians and Altitudes of a Triangle

∆ A B C, A B = A C

and

A L

is perpendicular to

B C

L

. In

∆ D E F, D E = D F

and

D M

is perpendicular to

E F

M

. If

(a r e a o f ∆ A B C) : (a r e a o f ∆ D E F) = 9.25

, then

\frac{D M + A L}{D M - A L}

is equal to:

Name the orthocentre of △PQR.

Important Questions on Properties of a Triangle

Learn and Prepare for any exam you want !

Name the orthocentre of $△ P Q R$ .