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Circles

Short Answer Type

111. Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.

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Long Answer Type

112.

In any triangle ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.

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Multiple Choice Questions

113. The longest chord of a circle is called

radius
diameter
segment
segment

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114. The centre of a circle lies

outside the circle
inside the circle
on the circle
on the circle

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115. How many circles can pass through three given non-collinear points?
one and only one
two
three
three

one and only one

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116. The measure of the angle of a semi-circle is

30°
45°
60°
60°

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117. The opposite angles of a cyclic quadrilateral

are complementary
are supplementary
are equal
are equal

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118. The angle of a minor segment is

acute
right
obtuse
obtuse

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119. In the following figure, ∠CAB = 40°, ∠AKB = 105°. The measure of ∠KCD is

72.5°
40°
35°
35°

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120. The degree measure of an angle of a segment of a circle is 60°. The degree measure of the angle subtended by the chord of the segment at the centre of the circle is