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.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 75

In

∆ A B C

,

A B = A C

. If the incircle of

∆ A B C

touches the sides of

B C, C A

and

A B

at

D, E

and

F

, then prove that

B E = F C

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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 D

,

A D

is perpendicular to

B C

and

C E

is perpendicular to

A B

. Prove that

A D : C E = A B : B C

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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

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10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 79

In a parallelogram

A B C D

the straight line drawn through

A

meets

B D, B C

and

D C

produced at

P, Q

and

R

. Prove that

A P^{2} = Q R

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