Line Segments that Subtends Equal Angles at Two Other Points

Q.

In the given figure, O is the centre of the circle, the value of x is

1. ${65}^{\circ }$

2. ${55}^{\circ }$

3. ${75}^{\circ }$

4. ${45}^{\circ }$

Q. Find the value of $x$ in the following figure.

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${90}^{\circ }$

Q. Find the value of $x$.

1. ${20}^{\circ }$
2. ${80}^{\circ }$
3. ${60}^{\circ }$

Q.

A, B, C, D are 4 non-collinear points in a plane such that $\angle$ ACB=$\angle$ ADB, then how many circle(s) can be drawn passing through all 4 points.

1. 0

2. 1

3. 2

4. 3

Q. Question 1
In the given figure, lines AB and CD intersect at O. if $\angle AOC+\angle BOE=70and\angle BOD={40}^{\circ },find\angle BOE$ and reflex $\angle COE.$

Q.

In the given figure, O is the centre of the circle, the value of x is

1. ${65}^{\circ }$

2. ${55}^{\circ }$

3. ${75}^{\circ }$

4. ${45}^{\circ }$

Q.

Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral ABCD is also cyclic.

$\left[4Marks\right]$

Q. Find the value of $\angle CAB+\angle CBA$ from the following figure.

1. ${130}^{\circ }$
2. ${80}^{\circ }$
3. ${100}^{\circ }$
4. ${50}^{\circ }$

Q. Question 3
In the given figure, $\angle PQR={100}^{\circ }$, where P, Q and R are points on a circle with centre O. Find $\angle OPR$.

Q. Draw a circle, Identify a point on it. Cut arcs on the circle with the length of the radius in succession. How many parts can the circle be divided into? Give reason.

Q. In the given figure $AB$ is diameter of a circle with centre. If $APQ$ and $RBQ$ are straight lines, $\angle A={35}^o$ and $\angle Q={25}^o$, find : (i) $\angle PRB$ (ii)$\angle PBR$ (iii) $\angle BPR$

Q. In a circle, $POQ$ is a diameter. "A" is a point on the circle and $\angle AOQ={70}^o$. Find the measure of the arc AQ.

1. ${40}^o$
2. ${50}^o$
3. ${70}^o$
4. None of the above

Q. In the circle shown above, chords $\overline{TR}$ and $\overline{QS}$ intersect at point P, which is the center of the circle, and the measure of $\angle PST$ is ${30}^{\circ }$. By the measurement of central angle calculate the measure of angle $RPS$

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$
5. Cannot be determined from the given information

Q. The diagram is drawn on triangular grids. $\Delta P^{\prime }{Q}^{\prime }{R}^{\prime }$ is the image of $\Delta PQR$ under a reflection.
On the diagram, it is possible to draw the line of reflection(Yes/No)

Q.

In the given figure, O is the centre of the circle, the value of x is

1. ${75}^{\circ }$

2. ${45}^{\circ }$

3. ${65}^{\circ }$

4. ${55}^{\circ }$

Q. P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle between the points P and Q. he tangents to the circle at the pints p and Q meet each other at the point S. If $\angle PSQ=20,\angle PRQ=?$

1. 80
2. 200
3. 160
4. 100