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Geometry - Circles

Multiple Choice Questions

O is the circumcentre of . If , , then is equal to

238 Views

If discount of 10% is given on the marked price of a radio, the gain is 20%. If the discount is increased to 20%, the gain is

222 Views

O is the centre of and , then the measure of is

125°
100°
130°
115°

236 Views

AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17cm. The length of AB and CD are 10 cm and 24 cm, respectively. The radius (in cm) of the circle is

529 Views

In the given figure, O is the centre, Then x, is equal to

$45 degree$
$55 degree$
$65 degree$
$65 degree$

240 Views

6.
AC is a chord of circle whose centre is at O. If B is any point on the arc AC and $angle OCA space equals space 20 degree$ , then the magnitude of $angle ABC$ is

$100 degree$
$40 degree$
$140 degree$
$140 degree$

140 degree

From figure,
OA = OC (radii of a circle)

$therefore$ $angle OAC space equals space angle OCA space equals space 20 degree$
In $increment AOC$ ,
$angle AOC space equals space 180 degree minus left parenthesis angle OAC plus angle OCA right parenthesis$
(by angle sum property of a triangle)
$equals 180 degree minus left parenthesis 20 degree plus 20 degree right parenthesis equals 180 degree minus 40 degree space equals space 140 degree$
Now, reflex $angle AOC space equals space 360 degree space minus space angle AOC$
$equals 360 degree minus 140 degree equals space 220 degree$
$therefore$ $angle ABC space equals space 1 half cross times space reflex space angle AOC$
$equals 1 half cross times 220 degree space equals space 110 degree$

380 Views

Two equal arcs of the two circles subtend angle of $60 degree$ and $75 degree$ at the centre. The ratio of the radii of the two circles is

$5 over 4$
$3 over 2$
$4 over 5$
$4 over 5$

221 Views

An angle in a semicircle is

$45 degree$
$60 degree$
$90 degree$
$90 degree$

156 Views

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is

8 cm
6 cm
4 cm
12 cm

1177 Views

10.

In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is

30°
45°
60°
60°

2540 Views

Previous Year Papers

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Multiple Choice Questions

6. AC is a chord of circle whose centre is at O. If B is any point on the arc AC and , then the magnitude of is

6.
AC is a chord of circle whose centre is at O. If B is any point on the arc AC and $angle OCA space equals space 20 degree$ , then the magnitude of $angle ABC$ is

$100 degree$
$40 degree$
$140 degree$
$140 degree$