Construction of Circle Segment

Q. Angle formed by an arc at the centre of a circle is ________ the angle formed by the same arc at it's circumference.

1. twice
2. equal
3. thrice
4. half

Q. The angle subtended by an arc at the circumference of a circle is ______ the angle at the centre.

1. twice
2. half
3. thrice
4. equal

Q.

PA and PB are tangents from P to the circle with center O. At point M which lies on circle, a tangent is drawn cutting PA at K and PB at N. Prove that KN = AK + BN. [2 MARKS]

Q.

Find the measure of $\angle ADC$ in the given figure.

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

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

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

4. ${75}^{\circ }$

Q. A line segment AB is of length 5cm. Draw a circle of radius 4 cm passing through A and B. Can you draw a circle of radius 2 cm passing through A and B? Give reason in support of your answer.

Q. 45. Prove that the angle subtended at the centre of a circle , is bisected by the radius passing through the mid point of the arc

Q. Question 8 (iv)
In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
$CM=\frac{1}{2}AB$

Q. Question 8
AB is a diameter and AC is a chord of a circle with centre O such that $\angle BAC={30}^{\circ }$. The tangent at c intersects extended AB at a point D. Prove that BC = BD.

Q. A segment of a circle is constructed with chord of length 5 cm and the angle subtented at a point on the circumference is ${60}^{\circ }$. Find the angles of the triangle formed by the centre of the circle and the chord.

1. ${120}^{\circ }$, ${50}^{\circ }$, ${70}^{\circ }$
2. ${60}^{\circ }$, ${30}^{\circ }$, ${90}^{\circ }$
3. ${60}^{\circ }$, ${60}^{\circ }$, ${60}^{\circ }$
4. ${120}^{\circ }$, ${30}^{\circ }$, ${30}^{\circ }$

Q. If ABC is an arc of a circle and ∠ABC = 135°, then the ratio of arc $\stackrel{⏜}{ABC}$ to the circumference is

(a) 1 : 4

(b) 3 : 4

(c) 3 : 8

(d) 1 : 2

Q.

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

1. 3 cm

2. 4 cm

3. 3.5 cm

4. 5 cm

Q. Draw a circle of radius 3 centimetres.
(a) Draw triangle ABC with this circle as circumcircle and angle ${50}^o,{60}^o$ and ${70}^o$.
(b) Construct triangle PQR, outside the circle, by drawing tangents to the circle at the points A, B and C.
(c) Find all angles of triangle PQR.

Q. Anshul now came back to draw. Now he took a scale and pencil. He drew something that looked like the figure shown below.

What did he draw?

1. Line
2. Circle
3. Line segment
4. Square

Q.

1. 60^o

2. 52.5^o

3. 75^o

4. 45^o

Q. In the given figure,

a chord BC of length 5 cm is the longest chord possible. if A is a point on the segment as shown, what kind of a triangle is $△$ABC?

1. right-angled
2. isosceles
3. equilateral
4. right-angled isosceles

Q.

Given three points, is it possible to construct a circle with all three on its circumference?

1. Only if they are non-collinear.

2. Only if they are in the same plane.

3. Only if they are concentric.

4. It is not possible.

Q.

Find the measure of $\angle ADC$ in the given figure.

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

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

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

4. ${75}^{\circ }$

Q. The radius of a circle with centre O is 7cm, OP = 4cm and OQ = 9cm state with reason which point lies in the interior and which in the exterior of the circle.

Q. In the figure, $CD$ is the diameter of a semicircle $CBED$ with centre $O$ and $AB$ $=$ $OD$. If $\angle EOD={60}^{\circ }$, then $\angle BAC$ is

1. ${15}^{\circ }$
2. ${20}^{\circ }$
3. ${30}^{\circ }$
4. ${45}^{\circ }$

Q. Can we draw a chord of 11cm in the circle of radius 5cm? Explain your answer.

Q. While constructing a $△XYZ$ with base $XY=10cm$ and $m\angle Z={30}^{\circ }$, you first need to draw the base $XY$ and then make an $\angle YXC$. Then measure of the $\angle YXC$ is:

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

Q. In the given figure, O is the centre of the circle and arc ABC subtends an angle of 130° at the centre. If AB is extended to P, find ∠PBC.

Q. A triangle ABC has its vertices lying on a circle, if $AB=24cm,BC=32cm$ and $AC=40cm$. Then find angle B.

1. ${90}^o$
2. ${45}^o$
3. ${180}^o$
4. $60$

Q.
What is the value of $\angle ACB$, if $\angle OAB={20}^{\circ }$ ?

1. 70

Q. A circle segment can be constructed if chord length and the ________ are given.

1. included angle
2. radius
3. arc length
4. All of the above.

Q. draw a circle of5.6 diameter

Q.
Circle has been constructed using chord AB subtending an angle of ${75}^{\circ }$. Value of $\angle OAB$ is

1. 15

Q. JKL is a tangent to the circle with centre O. Given that MK = MN and $\angle$LKN = 24${}^o$, find (a) $\angle$KON (b) $\angle$MKJ

Q. Question 16
In figure, $\angle ACB={40}^{\circ }$. Find $\angle OAB$.

Q. In given figure, O is the centre of a circle and ∠ABC = 45°. Prove that OA ⊥ OC.