Cyclic Quadrilateral

Q. Question 148
In rhombus BEAM, find $\angle AME$ and $\angle AEM$.

Q.

In the given figure A, B, C, and D, E, F are two sets of collinear points, Then AD $\parallel$ CF.

1. True

2. False

Q. Question 139
The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1 : 2. Can it be a parallelogram? Why or why not?

Q. Question 10
Which of the following properties describe a trapezium?
a) A pair of opposite sides is parallel
b) The diagonals bisect each other
c) The diagonals are perpendicular to each other
d) The diagonals are equal

Q.

ABCD is a cyclic quadrilateral of a circle with centre O such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle. If AD and BC produced meet at P, show that $APB={60}^{\circ }.$

Q.

In the given figure, SP is bisector of $\angle$ RPT and PQRS is a cyclic quadrilateral. Prove that :

SQ = SR.

Q.

How can I prove that a parallelogram ( which is not a rectangle ) is not cyclic????

Q.

A square pyramid is made using a square and four triangles with dimensions as shown below.

What would be the height of the pyramid?

What if the square and triangles are like these?

Q.

ABCD is a parallelogram with $\angle$ABC $={90}^{\circ }$, then number of right angles in the parallelogram excluding $\angle$ABC is/are ____

1. 2

2. 4

3. 3

4. cannot be found

Q.

In the figure, find the values of x and y hence show that $AB\parallel CD$. [3 MARKS]​

Q. if the non paralll sides of a trapezium are equal, prove that it is cyclic

Q.

In the given figure BD = DC and $\angle CBD={30}^{\circ }$, Find $\angle BAC$

1. ${20}^{\circ }$

2. ${90}^{\circ }$

3. ${60}^{\circ }$

4. ${10}^{\circ }$

Q.

1. Isosceles Trapezium

2. Trapezium

3. Square

4. Scalene Trapezium

Q.

In the given figure, if $\angle AOC={130}^{\circ },$ find the value of $\angle ABC$ . [3 Marks]

Q. If ABCD is a cyclic quadrilateral and $\angle A={90}^{\circ }-x^{\circ }$ , then $\angle C=$

1. 90o+xo
2. 90o - xo
3. 180o - xo
4. 90o + xo2

Q.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ }$ and $\angle BAC={30}^{\circ }$, then find $\angle BCD$. Further, if AB = BC, then find $\angle ECD$.

Q.

Match the following;
$\begin{array}{cc}Column-I& Column-II\\ \text{(A) In the given figure,}& \left(p\right){60}^{\circ }\\ \text{ABCD is a cyclic Quadrilateral.}& \\ \text{O is the centre of the circle.}& \\ \text{If}\angle BOD={160}^{\circ }\text{find the Measure of}\angle BPD.& \end{array}$


$\begin{array}{cc}\text{(B) In given figure, ABCD is a cyclic}& \left(q\right){65}^{\circ }\\ \text{quadrilateral whose side AB is a diameter}& \\ \text{of the circle through A, B, C, D.}& \\ \text{If}\angle ADC={130}^{\circ },\text{find}\angle BAC.& \end{array}$


$\begin{array}{cc}\text{(C) In the given figure BD = DC and}& \left(r\right){40}^{\circ }\\ \angle CBD={30}^{\circ }\text{Find m}\left(\angle BAC\right)& \end{array}$


$\begin{array}{cc}\text{(D) In the given figure, O is the centre of the}& \left(s\right){100}^{\circ }\\ \text{arc ABC subtends an angle of}{130}^{\circ }\text{at the centre.}& \\ \text{If AB is extended to Pm find}\angle PBC.& \end{array}$


Choose the correct option:

1. A-s; B-r; C-p; D-q

2. A-s; B-p; C-q; D-r

3. A-p; B-q; C-r; D-s

4. A-s; B-p; C-r; D-q

Q. The m$\angle ECB$ is :

1. ${43}^o$
2. ${45}^o$
3. ${75}^o$
4. ${40}^o$

Q.

In the given figure, RS is the diameter of the circle. NM is parallel to RS and $\angle MRS={29}^o$. Calculate $\angle NRM$

1. $\angle NRM={32}^o$

2. $\angle NRM={42}^o$

3. $\angle NRM={82}^o$

4. $\angle NRM={12}^o$

Q.

In the given figure A, B, C, and D, E, F are two sets of collinear points, Then AD $\parallel$ CF.

1. True

2. False

Q.

n the given figure, A, B, C, D are points on a circle centred at O.The lines AC and BD are extended to meet at P and lines AD and BC intersect at Q.Then find the relation of $\angle APB$, $\angle AQB$ and $\angle AOB$

Q. A flag staff on the top of a house subtends the same angle $\alpha$ at two points distant a and b from the house and on the same side of it. Prove that the length of flag-staff is $(a+b)\tan \alpha$.

Q. In the above figure, O is the centre of the circle. The angle CBD is equal to

1. ${25}^{\circ }$
2. ${40}^{\circ }$
3. ${50}^{\circ }$
4. ${130}^{\circ }$

Q. In the given figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of $\left(\angle ACD+\angle BED\right)$ (in degrees)

Q.

In the figure, given below, AD = BC,

$\angle BAC={30}^{\circ }$ and

$\angle CBD={70}^{\circ }$. Find $\angle BCD$

1. ${30}^{\circ }$

2. ${10}^{\circ }$

3. ${80}^{\circ }$

4. ${50}^{\circ }$

Q.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ },\angle BAC={30}^{\circ }$ and AB = BC, find $\angle ECD$.

1. ${50}^{\circ }$

2. ${70}^{\circ }$

3. ${60}^{\circ }$

4. ${40}^{\circ }$

Q.

In the given figure, RS is the diameter of the circle. NM is parallel to RS and $\angle MRS={29}^o$. Calculate $\angle RNM$

1. $\angle RNM={19}^o$

2. $\angle RNM={49}^o$

3. $\angle RNM={119}^o$

4. $\angle RNM={117}^o$

Q.

In the given figure, AB and CD are equal chords of a circle with centre O. If AB and CD intersect each other at right angle at point P and perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

Q. The given figure shows a parallelogram $ABED$. Points $P$ and $Q$ trisect the side $AB$, then
$area(△)=area\left(BQC\right)$
$=\frac{1}{6}\times area\left(/{/}_{gm}ABCD\right)$

1. True
2. False

Q.

Select the statements that are true.

1. $\angle CDB={49}^{\circ }$

2. $\angle ABC={43}^{\circ }$

3. $\angle ACB={88}^{\circ }$

4. $\angle ACB={28}^{\circ }$