Mathematics - Circles
Exam Duration: 45 Mins Total Questions : 30
AB is a chord of length 24 cm of a circle with centre O and radius 13 cm. Find the distance of the chord from the centre.
- (a)
5 cm
- (b)
6 cm
- (c)
\(\sqrt{407}\) cm
- (d)
25 cm
48 cm long chord of a circle is at a distance of 7 cm from the centre. Find the radius of the circle.
- (a)
5 cm
- (b)
17 cm
- (c)
25 cm
- (d)
16 cm
In the given figure, ΔABC is inscribed in a circle with centre O. lf ㄥACB = 65°, find ㄥABC.
- (a)
25°
- (b)
35°
- (c)
90°
- (d)
65°
An equilateral ΔPQR is inscribed in a circle with centre O. Find ㄥQOR..
- (a)
60°
- (b)
120°
- (c)
30°
- (d)
90°
Find the value of x in the following figure.
- (a)
45°
- (b)
35°
- (c)
60°
- (d)
55°
Two chords AB and CD of a circle cut each other when produced outside the circle at P. AD and BCarejoined. If ∠BAD = 30° and ∠CPA= 45°, find ∠CBP.
- (a)
105°
- (b)
115°
- (c)
135°
- (d)
75°
In the given figure, ΔABC is inscribed in a circle. The bisector of ㄥBAC meets BC at D and the circle at E. lf EC is joined and ㄥECD = 30°, find ㄥBAC.
- (a)
30°
- (b)
40°
- (c)
50°
- (d)
60°
In the given figure, POQ is a diameter of a circle with centre 0 and PQRS is a cyclic quadrilateral. SQ is drawn. If ㄥR = 138°, find ㄥPQS.
- (a)
90°
- (b)
42°
- (c)
48°
- (d)
38°
In the given figure, ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are drawn. If ㄥCAD = 40° and ㄥBDC = 25°, find ㄥBCD.
- (a)
85°
- (b)
120°
- (c)
115°
- (d)
95°
PQ and XY are two chords of a circle with centre O. If OA = OB, which of the following is correct?
- (a)
PQ > XY
- (b)
PQ < XY
- (c)
PQ II XY
- (d)
PQ = XY
A triangle ABC is inscribed in a circle, the bisectors of whose angles meet the circumference at X, Y and Z. Determine the angles X, Y and Z respectively.
- (a)
900-\(\frac{A}{2}\),900-\(\frac{B}{2}\),900-\(\frac{C}{2}\).
- (b)
90°,60°,30°
- (c)
\(\frac { A }{ 2 } ,\frac { B }{ 2 } ,\frac { C }{ 2 } \).
- (d)
\(\frac { B }{ 2 } ,\frac { A }{ 2 } ,\frac { A }{ 2 } -\frac { B }{ 2 } \).
Into how many parts does a circle divide a plane including itself?
- (a)
2 parts
- (b)
3 parts
- (c)
4 parts
- (d)
5 parts
Given two concentric circles with centre O. A line cuts the circles at A, B, C and D respectively. If AB = 10 cm, find the length of CD.
- (a)
5 cm
- (b)
10 cm
- (c)
7.5 cm
- (d)
15 cm
When are two circles said to be concentric?
- (a)
If they have the same radius
- (b)
If they have different radii.
- (c)
If they have the same centre
- (d)
If their centres are collinear.
In the given figure, \(\bar { PQR } =\bar { SRQ } \).
Which of the following is correct?
- (a)
PQ≠SR
- (b)
PS=QR
- (c)
PQ=SR
- (d)
PS≠QR
In the given figure. O is the centre of a circle having radius 5 cm. lf OM丄PQ and OM = 3 cm, find the length of chord PQ.
- (a)
5 cm
- (b)
8 cm
- (c)
10 cm
- (d)
6 cm
In the given figure, 0 is the centre of the circle and OM丄PO. If PQ = 6 cm and OM = 4 cm, find the radius of the circle.
- (a)
6 cm
- (b)
3 cm
- (c)
2 cm
- (d)
5 cm
In the given figure, O is the centre of the circle. If ㄥPOQ =110° and ㄥPOR= 120°, find ㄥQPR.
- (a)
65°
- (b)
55°
- (c)
50°
- (d)
60°
If O is the centre of the given circle with ㄥACB = 60°, find the value of x.
- (a)
120°
- (b)
100°
- (c)
240°
- (d)
180°
The given figure shows a circle with centre O in which a diameter AB bisects the chord PQ at the point R. lf PR= RQ= 8 cm and RB=4, cm find the radius of the circle.
- (a)
10 cm
- (b)
8 cm
- (c)
16 cm
- (d)
6 cm
In the given figure, 0 is the centre of the circle.
If ㄥABC=1100, find x.
- (a)
700
- (b)
1400
- (c)
600
- (d)
1200
In the given figure, ΔABC is an isosceles triangle with AB = AC and ㄥABC = 500 Find the sum of ㄥBDC and ㄥBEC.
- (a)
300
- (b)
600
- (c)
500
- (d)
1800
If the radius of a circle is 10 cm, find the length of a chord of the circle which is at a distance of 6 cm from its centre.
- (a)
16 cm
- (b)
10 cm
- (c)
12 cm
- (d)
14 cm
ABCD is a cyclic quadrilateral in which ㄥDBC = 55° and ㄥBAC = 55°. Find ㄥBCD.
- (a)
60°
- (b)
80°
- (c)
100°
- (d)
120°
In the given figure, AB = CD = 5 cm, OM = 3 cm. Then ON is _____________
- (a)
4 cm
- (b)
6 cm
- (c)
1.5 cm
- (d)
3 cm
In the given figure; O is the centre of the circle and \(\angle\)BDC = 42o . The measure of \(\angle\)BAC is ________
- (a)
42°
- (b)
48°
- (c)
58°
- (d)
52°
In the given figure, ABeD is a cyclic quadrilateral whose side AB is a diameter of the circle passing through A, B, C and D. If \(\angle\)ADC = 130°, find \(\angle\)BAC
- (a)
45°
- (b)
58°
- (c)
60°
- (d)
40°
In the given figure, AEDF is a cyclic quadrilateral. The values of x and y respectively are
- (a)
79°, 47o
- (b)
89°, 37o
- (c)
89o, 47o
- (d)
79o, 37o
o is the centre of the circle having radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. If OA meets BC at P then OP = ______
- (a)
3.6 cm
- (b)
1.4 cm
- (c)
2 cm
- (d)
3 cm
C1 is a circle of radius 6 cm, C2 is a circle of radius 8 cm. Jyoti wants the two circles to touch tangentially. She knows that there are two possibilities for the distance between their centres. What are these two distances?
- (a)
3 cm and 4 cm
- (b)
2 cm and 8 cm
- (c)
2 cm and 14 cm
- (d)
6 cm and 8 cm