SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 61

MEDIUM

10th West Bengal Board

IMPORTANT

Earn 100

The angular bisectors of the quadrilateral $P Q R S$ from a quadrilateral $A B C D$ . Prove that, $A B C D$ is a cyclic quadrilateral.

Important Questions on Miscellaneous Exercise : Geometry

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 61

A B C D

is an isosceles trapezium whose

(2)

. Prove that

A, B, C, D

are Concyclic

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 62

Two equal circles meet at

A

and

B

. The straight line through

A

A meets one circle at

P

and the other at

Q

. Prove that,

B P = B Q

.

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 62

In two circles the centre of one passes through the centre of the other. The two circles intersect at

A

and

B

. The straight line through

A

meets the two circles at

A B C D

and

Q

. Prove that,

△ P B Q

is equilateral.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 62

A B

is a common chord of two circles with centre

P

and

Q

. Prove that,

P Q

bisects

∠ A P B

and

∠ A Q B

.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 63

In a quadrilateral

A B C D

, the sum of angles

∠ A B C

and angle

∠ A D C

is

2

right angles and

A C

is the bisector of

∠ B A D

. Prove that,

B C = C D

.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 64

Prove that the sum of the angles in the three external circular parts of a triangle inscribed in a circle is

4

right angle.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 65

From an external point

P

,

P A

and

P B

are tangents drawn to a circle with centre

O

.

A

and

B

are points of contact. If

A C

is a diameter of the circle, then prove that

P O

is parallel to

B C

.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 30 - Miscellaneous Exercise : Geometry>Miscellaneous Exercise : Geometry>Q 66

Prove that the line joining the points of contact of two parallel tangents of a circle is a diameter of the circle.