Cyclic Quadrilateral

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. 3

3. 4

4. cannot be found

Q.

If a quadrilateral is cyclic, how many vertices of it should lie on the circle?

1. 1

2. 2
3. 3
4. 4

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.

ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle. If $\angle ADC={130}^{\circ }$, find $\angle BAC$.

1. 30º

2. 50º

3. 60º

4. 40º

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.

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.

Select the statements that are true.

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

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

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

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

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.

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.

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