Examination Questions in Geometry --Circles

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 :
a. 60° b.100° c.120° d. 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. a right angle triangle
b. an equilateral triangle
c. an isosceles triangle
d. a scalene triangle

3. The minimum numbers of common tangents drawn to two circles when both the circle touch externally is :
a. 0, b. 1 c. 2 d. 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
a. 120° b. 60° c. 75° d. 150°

5.ABCD is a cyclic quadrilateral, AB is a diameter of the circle. If angle ACD = 50° , the value of angle BAD is
a. 30° b. 40° c. 50° d. 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
a. TQ < TR b. TQ > TR
c. TQ= 2 TR d. 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 = ?
a. 20° b. 30° c. 40° d. 60°

ANSWERS::1-C, 2-B, 3-B, 4-A, 5-B, 6-7-D

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