EASY

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The diagonal of a cyclic square is a radius of the circle.

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Important Questions on Circles

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

$O$ is the centre of a circle and $A B$ a diameter. $A B C D$ is a cyclic quadrilateral. $∠ A B C = 65 °$ , $∠ D A C = 40 °$ then the measure of $∠ B C D$ is

HARD

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

ABCD is cyclic quadrilateral. Sides AB and DC, when produced, meet at E, and sides BC and AD, when produced, meet at F. If

∠ B F A = 60 ° and ∠ A E D = 30 °,

then the measure of

∠ A B C

is _____.

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

∠ A = 100 °

of a cyclic quadrilateral

A B C D

, then the value of

∠ C

is:

MEDIUM

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

A B C D

is a cyclic quadrilateral. Diagonals

B D

and

A C

intersect each other at

E

. If

∠ B E C = 138 °

and

∠ E C D = 35 °

, then what is the measure of

∠ B A C

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

P Q R S

is a cyclic quadrilateral in which

P Q = x c m, Q R = 16.8 c m, R S = 14 c m, P S = 25.2 c m

and

P R

bisects

Q S

. What is the value of

x

MEDIUM

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

The side

A B

and

D C

of a cyclic quadrilateral

A B C D

are produced to meet at

E

and sides

A D

and

B C

are produced to meet at

F

. If

∠ A D C = 78 °

and

∠ B E C = 52 °

, then find the measure of

∠ A F B

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

If all the four vertices of a quadrilateral

A B C D

lie on the circle and

m ∠ D = 60 °

then

m ∠ B =

_____.

MEDIUM

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

It is known that area of a cyclic quadrilateral is

\sqrt{(s - a) (s - b) (s - c) (s - d)}

where

a, b, c, d

are the sides and

s = \frac{a + b + c + d}{2}

. If a circle can also be inscribed in the cyclic quadrilateral then the area of this quadrilateral is

HARD

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

Sides

A B

and

D C

of a cyclic quadrilateral

A B C D

are produced to meet at

E

, and sides

A D

and

B C

are produced to meet at

F

. If

∠ A D C = 75 °

,and

∠ B E C = 52 °

, then the difference between

∠ B A D

and

∠ A F B

is:

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

A B C D

is a cyclic quadrilateral in which sides

A D

and

B C

are produced to meet at

P

, and sides

D C

and

A B

meet at

Q

when produced. If

∠ A = 60 °

and

∠ A B C = 72 °

, then

∠ D P C - ∠ B Q C =

MEDIUM

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

A B C D

is a cyclic quadrilateral in which

A B = 14.4 cm, B C = 12.8 cm

and

C D = 9.6 cm

. If

A C

bisects

B D

, then what is the length of

A D

MEDIUM

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

Let

A B C D

be a quadrilateral such that there exists a point

E

inside the quadrilateral satisfying

A E = B E = C E = D E

. Suppose

∠ D A B, ∠ A B C, ∠ B C D

is an arithmetic progression. Then the median of the set

\{∠ D A B, ∠ A B C, ∠ B C D\}

is :-

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

In figure $P Q$ , is a chord of a circle with centre $O$ and $P T$ is its tangent at $P$ . if $∠ Q P T = 60 °$ , then $∠ P R Q$ is

Question Image

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

The sum of pairs of opposite angles of a cyclic quadrilateral is

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

In the figure, points $P, Q, R$ and $S$ lie on a circle. Then the values of $x$ and $y$ are respectively

Question Image

MEDIUM

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

ABCD is a cyclic quadrilateral in which

∠ A = x °, ∠ B = 5 y °, ∠ C = 2 x ° and ∠ D = y °

. what is the value of

(3 x - y) ?

MEDIUM

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

ABCD is acyclic quadrilateral such that when sides AB and DC are produced, they meet at E, and sides AD and BC meet at F, when produced. If

∠ A D E = 80 ° and ∠ A E D = 50 °

, then what is measure of

∠ A F B ?

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

In the figure, if $∠ A = 100^{\circ}$ then $∠ C =$ ?

Question Image

EASY

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

A B C D

is a cyclic quadrilateral in which

A B = 16.5 c m

B C = x c m

C D = 11 c m

A D = 19.8 c m

B D

is bisected by

A C

O

. What is the value of

x

HARD

Mathematics>Geometry>Circles>Cyclic Quadrilaterals

The points

A, B, C, D, E

are marked on the circumference of a circle in clockwise direction such that

∠ A B C = 130^{o} a n d ∠ C D E = 110^{o} .

The measure of

∠ A C E

in degree is

The diagonal of a cyclic square is a radius of the circle.

Important Questions on Circles

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