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Grade 9 Exam  >  Grade 9 Tests  >  Test: Properties of Equal Chords - Grade 9 MCQ

Test: Properties of Equal Chords - Grade 9 MCQ


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10 Questions MCQ Test - Test: Properties of Equal Chords

Test: Properties of Equal Chords for Grade 9 2024 is part of Grade 9 preparation. The Test: Properties of Equal Chords questions and answers have been prepared according to the Grade 9 exam syllabus.The Test: Properties of Equal Chords MCQs are made for Grade 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
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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
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In the given figure, the measure of angle BCD is

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Test: Properties of Equal Chords - Question 3
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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
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Chords of a circle, equidistant from the centre are
Test: Properties of Equal Chords - Question 5
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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
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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
Detailed Solution for Test: Properties of Equal Chords - Question 6

Given: ∠BOA=90∘ and ∠AOC=110∘

We know that angles around a point add up to 360∘

∴∠BOC+∠BOA+∠AOC=360∘

⇒∠BOC+90∘+110∘=360∘

⇒∠BOC=360∘−200∘

∠BOC=160∘

We know that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

Arc BC is subtending ∠BOC at the center and ∠BAC on the remaining part of the circle, so ∠BOC=2×∠BAC

Test: Properties of Equal Chords - Question 7
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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
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In the figure, angle ABC = 65° and angle ACB = 58°, the measure of angle BDC is
Test: Properties of Equal Chords - Question 9
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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
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In the given figure, angle OAC is 35°, angle ADC is
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