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In $△ A B C, ∠ A = 90^{0} .$ $D$ is the mid point of $A C$ . Prove that $B C^{2} - B D^{2} = 3 A D^{2} .$

Important Questions on The Triangle and its Properties

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

BD and CE are the medians of

△ A B C

, right angles at A. If CE

= \frac{5 \sqrt{13}}{2} cm

, BC

= 10 cm

, then the length of BD is ____.

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

In the figure, $∠ A B C = 90 °, ∠ C = ∠ D = 45 °, A B = 10 cm$ . What is the length of $A C$ ?

Question Image

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

In the figure, $∠ A B C = 90 °, ∠ C = ∠ D = 45 °, A B = 10 cm$ . What is the radius of the circumcircle of triangle $A B D$ ?

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MEDIUM

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

Triangles ABC and DBC are right-angled triangles with common hypotenuse BC, BD, and AC intersect at P when produced. If

PA = 8 cm, PC = 4 cm

and

PD = 3.2 cm

, then the length of BD in cm is:

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

∆

P Q R

measure of angle

Q

90^{o}

. If

\tan P = \frac{24}{7}

and

P Q = 14 c m

, then what is the length of side

Q R

in cm.

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

In triangle ABC, if

∠ B = 90 °, A B = 21 cm and BC = 20 cm

, then

\frac{1 + \sin A - \cos A}{1 + \sin A + \cos A}

is equal to:

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

In the figure, $∠ A B C = 90 °, ∠ C = ∠ D = 45 °, A B = 10 cm$ . What is the radius of the circumcircle of triangle $A B C$ ?

Question Image

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

A B C

is a triangle right angled at

B

. Let

D

be the midpoint on

A C

. If

B D = 6.5 c m

, then what is

A B^{2} + B C^{2}

is equal to?

MEDIUM

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

∆ A B C, ∠ A = 90 °

M

is the midpoint of

B C

and

D

is the point on

B C

such that

A D ⊥ B C

. If

A B = 7 c m

and

A C = 24 c m

, then

A D : A M

is equal to?

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

Δ ABC, A B = c cm, A C = b cm

and

C B = a cm

. If

∠ A = 2 ∠ B

, then which of the following is true?

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

Point M and N are on the sides PQ and QR respectively of a triangle PQR, right angled at Q. If

PN = 9 cm, MR = 7 cm, and MN = 3 cm

, then find the length of PR (in cm).

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

∆

D E F

is right angled at E. If m

∠ F = 30^{o}

, then find the value of

[\cos D - \frac{1}{\sqrt{2}}]

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

Let ABC be a triangle right-angled at C, then what is

\tan A + \tan B

equal to?

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

What is the perimeter of a right-angled triangle whose sides (making

90 °

) are

20 \sqrt{3} cm and 15 \sqrt{3} cm

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

ABC is a triangle right angled at A and AD is perpendicular to BC. If

BD = 8 cm and DC = 12.5 cm

, then what is AD equal to?

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

The circle of radius

4 c m

and centre

O

has a tangent

P R

. If

∠ P O R = 90^{o}

and

O R = 7 c m

and

O P = 24 c m

. Calculate the length (in

c m

.) of

P R

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

Triangle ABC is right-angled at A and AD is perpendicular to BC. If BD

= 7.5 cm

and DC

= 10 cm

, then what is AD equal to?

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

State Pythagoras theorem.

MEDIUM

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

For a Right angled triangle, two connected sides are 1.5 & 2 cm. Find the area of circumcircle?

EASY

Mathematics>Geometry>The Triangle and its Properties>Right Angled Triangles and Pythagoras Property

△ A B C,

the measure of angle

∠ A B C

90 °

. If

tan A = \frac{12}{5},

and

A B = 1 c m

, then what is the length (in

c m

) of side

B C ?

In △ABC, ∠A = 900. D is the mid point of AC. Prove that BC2-BD2=3 AD2.

Important Questions on The Triangle and its Properties

Learn and Prepare for any exam you want !

In $△ A B C, ∠ A = 90^{0} .$ $D$ is the mid point of $A C$ . Prove that $B C^{2} - B D^{2} = 3 A D^{2} .$