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Grade 9 Exam  >  Grade 9 Tests  >  Test: Angle Subtended By The Chord - Grade 9 MCQ

Test: Angle Subtended By The Chord - Grade 9 MCQ


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20 Questions MCQ Test - Test: Angle Subtended By The Chord

Test: Angle Subtended By The Chord for Grade 9 2024 is part of Grade 9 preparation. The Test: Angle Subtended By The Chord questions and answers have been prepared according to the Grade 9 exam syllabus.The Test: Angle Subtended By The Chord MCQs are made for Grade 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Angle Subtended By The Chord below.
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Test: Angle Subtended By The Chord - Question 1
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Any angle whose vertex is at the centre of the circle is called

Test: Angle Subtended By The Chord - Question 2
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In the given figure, if ∠OAB = 40o then ∠ACB is equal to:

Detailed Solution for Test: Angle Subtended By The Chord - Question 2

In triangle OAB

OA = OB (radius of a circle)

∠OAB = ∠OBA

∠OBA = 40º (angles opposite to equal sides are equal)

Using the angle sum property

∠AOB + ∠OBA + ∠BAO = 180º

Substituting the values

∠AOB + 40º + 40º = 180º

By further calculation

∠AOB + 80º = 180º

∠AOB = 180º - 80º

∠AOB = 100º

As the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle

∠AOB = 2 ∠ACB

Substituting the values

100º = 2 ∠ACB

Dividing both sides by 2

∠ACB = 50º

Therefore, ∠ACB is equal to 50º.

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Test: Angle Subtended By The Chord - Question 3
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If the angles subtended by the chords of a circle at the centre are equal, then the chords are

Test: Angle Subtended By The Chord - Question 4
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Name the chord that subtends angle FOE at the centre.
Test: Angle Subtended By The Chord - Question 5
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In the given figure name the angle subtended by the chord PQ on the major arc
Test: Angle Subtended By The Chord - Question 6
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The angles subtended by arcs XY and MN on the centre of the circle are 72° each. The length of chord XY = 15 cm, then the length of chord MN is:
Test: Angle Subtended By The Chord - Question 7
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In a circle with center O and a chord BC, points D and E lie on the same side of BC. Then, if∠BDC=80°, then ∠BEC =
Test: Angle Subtended By The Chord - Question 8
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In a circle with center O and a chord BC, the point D lies on the same side BC as O. If ∠ BOC = 50°,then ∠ BDC =
Test: Angle Subtended By The Chord - Question 9
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In the figure, O and O' are centres of two circles intersecting at B aand C. ACD is a straight line, find x.
Detailed Solution for Test: Angle Subtended By The Chord - Question 9

In the figure, two circle with centers O and O' intersect each other at B and C.

ACD is a line, ∠AOB=130∘

Arc AB subtends ∠AOB at the centre O and ∠ACB at the remaining part of the circle.

Test: Angle Subtended By The Chord - Question 10
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A regular octagon is inscribed in a circle. The angle that each side of the octagon subtends at the centre is
Test: Angle Subtended By The Chord - Question 11
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In the given figure, what is the measurement of YXZ?
Detailed Solution for Test: Angle Subtended By The Chord - Question 11

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Test: Angle Subtended By The Chord - Question 12
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In figure, O is the centre of the circle and PS bisects ∠QPR. Find ∠QRS.
Test: Angle Subtended By The Chord - Question 13
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An equilateral triangle ABC is inscribed in a circle with centre O. Angle BOC will be
Test: Angle Subtended By The Chord - Question 14
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In figure arc PQ = arc PR, ∠POQ = 30° and ∠QOS = 70°. Find ∠ROS.
Detailed Solution for Test: Angle Subtended By The Chord - Question 14
Sol^ :- Join RP and PQ. then, RP=PQ [ Since *arc RP=arcPQ* ] Now since segment RP=PQ Then, ∠POR =∠POQ = 30* [ Angles of same or equal segment ] Now, ∠ROS = ∠POQ+∠POR+∠QOS ∠ROS = 30*+30*+70* ∠ROS = 130* 《* represents DEGREE》
Test: Angle Subtended By The Chord - Question 15
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Chord AB subtends ∠AOB = 60° at centre. If OA = 5 cm then length of AB (in cm) is :
Test: Angle Subtended By The Chord - Question 16
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In the figure, ∠M = 82°, then ∠O = ?
Test: Angle Subtended By The Chord - Question 17
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If ∠OAB = 40° then ∠ACB is equal to:
Detailed Solution for Test: Angle Subtended By The Chord - Question 17

In ΔQAB, OA = OB [both are the radius of a circle]
∠OAB = ∠OBA ⇒ ∠OBA = 40°
[angles opposite to equal sides are equal] Also, ∠AOB + ∠OBA + ∠BAO = 180°
[by angle sum property of a triangle]
∠AOB + 40° + 40° = 180°
⇒ ∠AOB = 180° – 80° = 100°
We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
∠AOB = 2 ∠ACB ⇒ 100° =2 ∠ACB
∠ACB = 100°/2 = 50°

Test: Angle Subtended By The Chord - Question 18
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In the figure, if AB is the diameter of the circle, then the value of x is:
Test: Angle Subtended By The Chord - Question 19
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An equilateral ΔABC is inscribed in a circle with centre O. The measure of ∠BOC is:
Test: Angle Subtended By The Chord - Question 20
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If the regular polygon is inscribed in a circle the sum of all the angles are at the the centre is
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