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This mock test of Test: Properties Of Equal Chords for Class 9 helps you for every Class 9 entrance exam.
This contains 10 Multiple Choice Questions for Class 9 Test: Properties Of Equal Chords (mcq) to study with solutions a complete question bank.
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QUESTION: 1

XY and PQ are two parallel chords of a circle on opposite side of the centre O and radius of circle is 13 cm. if PQ = 10 cm and XY = 24 cm, find the distance between PQ and XY.

Solution:

QUESTION: 2

In the given figure, the measure of angle BCD is

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QUESTION: 3

In the following figure, ∠FEG = 37.5°, find the OFG.

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QUESTION: 4

Chords of a circle, equidistant from the centre are

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QUESTION: 5

In the figure, O is the centre of the circle and the measure of arc ABC is 100^{o}. The measure of angle ABC will be

Solution:

QUESTION: 6

A, B and C are three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 90° and 110° respectively. Then the measure of angle BAC is

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QUESTION: 7

The angle which, an arc of a circle subtends at the centre is ….. the angle which it subtends at any point on the remaining part of the circumference.

Solution:

Given : An arc ABC of a circle with center O , and a point C on the remaining part of the circumference.

To Prove : Angle AOB = Twice angle ABC

Construction : Join OC and produce it to a suitable point D

Proof : Let angles 1,2,3,4,5,6 be as shown in figure

a) OA=OB=OC [RADII OF THE SAME CIRCLE ARE EQUAL]

b)1=4,2=3 [ANGLES OPPOSITE TO EQUAL SIDES ARE EQUAL]

c)5=4+1=Twice angle1 [EXTERIOR ANGLE PROPERTY]

d)6=2+3=Twice angle 2 [EXTERIOR ANGLE PROPERTY]

e)5+6=Twice angle (1+2) [ADD STATEMENT c AND d]

f)Angle AOB = Twice angle ACB [WHOLE = SUM OF ALL ITS PARTS]

QUESTION: 8

In the figure, angle ABC = 65° and angle ACB = 58°, the measure of angle BDC is

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QUESTION: 9

Two equal chords AB and CD of a circle are such that the length of perpendicular OE on CD = 5 cm. If OF is the perpendicular on AB, then OF =

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QUESTION: 10

In the given figure, angle OAC is 35°, angle ADC is

Solution:

### Equal Chords Theorem - Theorem on Circles CBSE Class IX ICSE Class X

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