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Test: Properties of Equal Chords - Class 9 MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Properties of Equal Chords

Test: Properties of Equal Chords for Class 9 2024 is part of Mathematics (Maths) Class 9 preparation. The Test: Properties of Equal Chords questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Properties of Equal Chords MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Properties of Equal Chords below.
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Test: Properties of Equal Chords - 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.

Test: Properties of Equal Chords - Question 2

In the given figure, the measure of angle BCD is

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Test: Properties of Equal Chords - Question 3

In the given figure ∠SOR = 37.5° find the value of ∠PTQ.

Detailed Solution for Test: Properties of Equal Chords - Question 3

∠SOR = 37.5° 

∠SQT = 1/2 ∠SOR (Angle at the circumference is half of the angle at the centre)

⇒ 37.5°/2

⇒ 18.75°                                                                                             

∠QSP = 90° (angle made from the diameter to the circumference is 90°)

Now,

∠PSQ + ∠QST = 180° (Linear pair angle)

∠QST = 180° - 90° = 90°

In ∆QST,

∠STQ = 180° - (90° + 18.75°)

⇒ ∠STQ = 71.25°

Test: Properties of Equal Chords - Question 4

Chords of a circle, equidistant from the centre are

Test: Properties of Equal Chords - Question 5

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

Test: Properties of Equal Chords - 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

Test: Properties of Equal Chords - 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.

Detailed Solution for Test: Properties of Equal Chords - Question 7
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]

Test: Properties of Equal Chords - Question 8

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

Test: Properties of Equal Chords - 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 =​

Test: Properties of Equal Chords - Question 10

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

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