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

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10th West Bengal Board

IMPORTANT

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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

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 76

Prove that in a quadrilateral circumscribing a circle, the angle made by any two opposite sides at the centre are complementary.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 76

A B

and

A C

are two tangents to a circle from an external point

A

.

P

is the point on the arc

B C

and the tangent at

P

intersects

A B

and

A C

at

D

and

E

. Prove that the perimeter of

∆ A D E

is

2 A B

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 76

A B

is a diameter of a circle and

C

is a point on circumference.

D

is the foot of perpendicular from

A

upon the tangent at

C

. Prove that

∠ C A B = ∠ C A D

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10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 77

P T

is a tangent at

P

to a circle with centre

O

and the chord

P A

lies on the same side of the centre

O

.

B

lies on the circle such that

∠ A P B = 1

right angle. Prove that,

∠ A B P = ∠ A P T

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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

,

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

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