SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 73

MEDIUM

10th West Bengal Board

IMPORTANT

Earn 100

If two equal chords of a circle intersect, prove that the two parts of one chord is equal to the two parts of the other chord.

Important Questions on Miscellaneous Exercise : Geometry

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 74

Prove that a chord of a circle make equal angles with the tangents at its ends.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 78

In a triangle

∆ A B C

,

A D

is perpendicular to

B C

and

∵ A M = D N = \frac{1}{2} A B = \frac{1}{2} C D

is perpendicular to

A B

. Prove that

A D : C E = A B : B C

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 78

In

∆ A B C

, the bisector of

∠ A B C

meets

A C

at

P

. Prove that

B C : B A = C P : P A

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 80

Two circles touch externally. A straight line through the point of contact meets the circle in two points

P

and

Q

. Prove that, the radii through

P

and

Q

are parallel.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 80

Two circles touch externally. A straight line through the point of contact meets the circle in two points

P

and

Q

. Prove that, the tangents at

P

and

Q

are parallel.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 81

In

∆ A B C

,

∠ A

ia right angle and

A D ⊥ B C

. Prove that

A B^{2} = B C . B D

and

A C^{2} = B C . B D

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 82

In

∆ A B C,

the points

D, E, F

are taken on

A B, A C

and

B C

in such a way that

D E ∥ B C

and

E F ∥ A B

. Prove that,

\frac{A B}{A D} = \frac{B C}{B F}

.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 83

∆ A B C

and

∆ D B C

lie on the same side of the base

B C

. Three points

E, F

and

G

on

B C, A C

and

A D

are taken in such a way that

E F ∥ B A

and

E G ∥ B D

. Prove that

F G ∥ A D