SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 5

MEDIUM

10th West Bengal Board

IMPORTANT

Earn 100

In a $∆ A B C$ , the perpendicular from $A$ upon $B C$ meets $B C$ at $D$ . Prove that $B D^{2} - C D^{2} = A B^{2} - A C^{2}$ .

Important Questions on Pythagoras' Theorem

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 6

In

∆ A B C, A B = A C

and

B D ⊥ A C

. Prove that

B D^{2} - C D^{2} = 2 C D \times A D

.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 7

In an isosceles triangle

A B C

. If

B C

is produced to

D

, then prove that

A D^{2} - A C^{2} = B D \times C D

.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 8

In

∆ A B C

,

∠ A

is a right angle.

P

and

Q

are any points on

A B

and

A C

. Prove that,

B Q^{2} + P C^{2} = B C^{2} + P Q^{2}

.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 9

In

∆ A B C, ∠ A

is a right angle.

B E

and

C F

are two medians. Prove that

5 {(B C)}^{2} = 4 (B E^{2} + C F^{2})

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10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 10

In $∆ A B C, ∠ A$ is a right angle. $D$ and $E$ are the midpoints of $A B$ and $A C$ . Prove that, $B E^{2} + C D^{2} = 5 D E^{2}$ .

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 12

In

∆ A B C, ∠ A = 90 °

. The perpendicular from

A

upon

B C

meets

B C

at

D

. If

B C = 9 c m, B D = 4 c m

, then find the length of

A B

.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 13

O

is the centre of a circle. From an external point

P

a straight line is drawn to meet the circle at

B

and

A

. Prove that,

P A \times P B = P O^{2} - r^{2}

, where

r

is the radius of the circle.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 16 - Pythagoras' Theorem>EXERCISE 6>Q 14A

The diagonals of a rhombus are

5 cm

and

12 cm

, then the length of the side of a rhombus is