### Examination Questions in Geometry - Circles

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1. Each of the two circles of equal radii with centres at A and B pass through the centre of one another. If they cut at C and D then angle DBC is equal to :

- 60°
- 100°
- 120°
- 140°

2. The three equal circles touch each other externally. If the centres of these circles be A, B, C then triangle ABC is :

- a right angle triangle
- an equilateral triangle
- an isosceles triangle
- a scalene triangle

3. The minimum numbers of common tangents drawn to two circles when both the circle touch externally is :

- 0
- 1
- 2
- 3

4. A, B, P are three points on a circle having centre O. If angle OAP = 25° and angle OBP = 35°, then the measure of angle AOB is

- 120°
- 60°
- 75°
- 150°

5. ABCD is a cyclic quadrilateral, AB is a diameter of the circle. If angle ACD = 50° , the value of angle BAD is

- 30°
- 40°
- 50°
- 60°

6. Two circles of equal radii touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. The relation of TQ and TR is

- TQ < TR
- TQ > TR
- TQ = 2 TR
- TQ = TR

7. AB is the chord of a circle with centre O and DOC is a line segment originating from a point D on the circle and intersecting AB produced at C such that BC = OD. If angle BCD = 20° , then angle AOD = ?

- 20°
- 30°
- 40°
- 60°

8. In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. If both the chords are on the same side of the centre, then the distance between the chords is

- 9 cm
- 7 cm
- 23 cm
- 11 cm

9. O is the centre of the circle passing through the points A, B and C such that angle BAO = 30^{o}, angle BCO = 40^{o} and angle AOC = x^{o}. What is the value of x?

- 70
^{o} - 140
^{o} - 210
^{o} - 280
^{o}

10. The diameter of a circle with centre at C is 50 cm. CP is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP = 18 cm, then what is the length of AB?

- 24 cm
- 32 cm
- 40 cm
- 48 cm