Explore Exams
Login Signup
Sign in Open App
CBSE Class 9  >  Class 9 Test  >  Online MCQ Tests  >  Test: Cyclic Quadrilaterals - Class 9 MCQ

Cyclic Quadrilaterals - Free MCQ Practice Test with solutions, Class 9


MCQ Practice Test & Solutions: Test: Cyclic Quadrilaterals (15 Questions)

You can prepare effectively for Class 9 Online MCQ Tests for Class 9 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Cyclic Quadrilaterals". These 15 questions have been designed by the experts with the latest curriculum of Class 9 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

Sign up on EduRev for free to attempt this test and track your preparation progress.

Test: Cyclic Quadrilaterals - Question 1
Save

In the given figure, ∠M is 75° then ∠O is equal to.

Detailed Solution: Question 1

We know that, sum of all angles of rectangle =360° so, the sum of 2 angles of rectangle = 360°\2 = 180°  Angle A + Angle B=180°

  75+B=180°

or, B=180-75°

or, B=105 degree.

Test: Cyclic Quadrilaterals - Question 2
Save

A, B, C and D are four points on a circle. AC and BD intersect at E such that angle BEC =140° and angle ECD = 25°, then angle BAC is

Detailed Solution: Question 2

Using the cyclic quadrilateral property:

∠BEC + ∠BAC = 180∘

Substitute the value of ∠BEC=140∘:

∠BAC = 180∘−140∘= 40∘

∠ECD is an exterior angle to triangle △CED.

  • By the Exterior Angle Property:

∠ BEC = ∠BAC + ∠ECD

140∘=∠BAC+25∘

∠BAC = 140∘−25∘=115∘

Clear all your doubts with EduRev
Test: Cyclic Quadrilaterals - Question 3
Save

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angle DBC = 55° and angle BAC = 45°, the measure of angle BCD is

Detailed Solution: Question 3

∵∠BAC and ∠BDC are in the same segment.

∴ ∠BAC=∠BDC=45∘

Now in ΔBCD, ∠DBC+∠BDC+∠BCD=180∘ (Sum of angles of a triangle)

⇒55∘+45∘+∠BCD=180∘

⇒100∘+∠BCD=180∘

⇒∠BCD=180∘−100∘ = 80∘

Hence, ∠BCD=80∘

Test: Cyclic Quadrilaterals - Question 4
Save

In the figure, triangle ABC is an isosceles triangle with AB = AC and measure of angle ABC = 50°. Then the measure of angle BDC and angle BEC will be

Detailed Solution: Question 4

Test: Cyclic Quadrilaterals - Question 5
Save

In the figure, quadrilateral PQRS is cyclic. If ∠P = 80°, then ∠R =

Detailed Solution: Question 5

Property of Cyclic Quadrilateral: In a cyclic quadrilateral, the sum of opposite angles is always 180°:

∠P + ∠R = 180∘

Given ∠P = 80∘, substitute into the equation:

80∘+∠R =180∘

Rearranging the equation:

∠R = 180∘−80∘=100∘

Test: Cyclic Quadrilaterals - Question 6
Save

If AB = 12 cm, BC = 16 cm and AB ⊥ BC, then radius of the circle passing through A,B and C is

Detailed Solution: Question 6

Test: Cyclic Quadrilaterals - Question 7
Save

In the figure, ABC is an equilateral triangle. Measure of angle BEC is

Detailed Solution: Question 7

Test: Cyclic Quadrilaterals - Question 8
Save

In the figure, ∠M = 82°, then O = ?

Detailed Solution: Question 8

The sum of opposite angles of a cyclic quadrilateral is 180°.

M + O=180°

O=180°- 82°= 98°

Test: Cyclic Quadrilaterals - Question 9
Save

In a circle, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced to F. If ∠ABC = 85° and ∠FAE = 24°, find the value of ∠BCD.

Detailed Solution: Question 9

We know that 

∠ABC = 85°  
∠FAE = 24°  
AE is parallel to CD  
AB is produced to F  

Formula Used:  
In a cyclic quadrilateral, opposite angles sum up to 180°.  
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.  

Calculation:  

We know in a cyclic quadrilateral opposite angles sum up to 180°. So,  
∠ABC + ∠ADC = 180°  
∠ADC = 180° - 85° = 95°  
∠EAD = ∠ADC = 95° [Alternate interior angles of parallel lines CD and AE]  
∠FAD = ∠FAE + ∠EAD  
∠FAD = 24° + 95° = 119°  
∠BCD = ∠FAD = 119° [Exterior angle of a cyclic quadrilateral]  

∴ The correct answer is 119°.
 

Test: Cyclic Quadrilaterals - Question 10
Save

If ∠C = ∠D = 50° then four points A, B, C, D:

Detailed Solution: Question 10

Definition of Concyclic Points: Four points are said to be concyclic if they lie on the circumference of a single circle. In such a case, the opposite angles of the quadrilateral formed by these points are supplementary:

∠C+∠A=180∘ and ∠D+∠B=180∘

Analyze ∠C+∠A

From the figure, ∠A is the angle opposite to ∠C. The condition for cyclic quadrilaterals is:

∠C+∠A=180∘

Substitute ∠C=50∘:

50∘+∠A=180∘

Solve for ∠A:

∠A = 180∘− 50∘=130∘

 Analyze ∠D+∠B

Similarly, ∠B is opposite to ∠D. The condition for cyclic quadrilaterals is:

∠D+∠B = 180∘

Substitute ∠D=50∘

50∘+∠B = 180∘

Solve for ∠B:

∠B=180∘−50∘=130∘

 Check Concyclicity

  • Opposite angles ∠C+∠A=180∘
  • Opposite angles ∠D+∠B=180∘

Since the opposite angles of quadrilateral ABCD are supplementary, the quadrilateral is cyclic. Therefore, the four points A,B,C,D are concyclic and lie on the circumference of a single circle.

Test: Cyclic Quadrilaterals - Question 11
Save

In the figure, angle BAD = 75°, angle DCF = x and angle DEF = y.The values of x and y are

Detailed Solution: Question 11

We know that if one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior
opposite angle.
i.e., ∠BAD = ∠DCF = 75°
⇒ ∠DCF = x = 75 °
Again, the sum of opposite angles in a cyclic quadrilateral is 180 °.
Thus, ∠DCF + ∠DEF = 180°
⇒ 75° + y = 180°
⇒ y = (180° - 75°) = 105°
Hence, x = 75° and y = 105°

Test: Cyclic Quadrilaterals - Question 12
Save

If the sum of a pair of opposite angles of a quadrilateral is 180o, the quadrilateral is:

Detailed Solution: Question 12

A quadrilateral is called cyclic if all the four vertices of it lie on a circle and the sum of either pair of opposite angles of a cyclic quadrilateral is 180∘.

Here,∠1+∠2=180∘

Test: Cyclic Quadrilaterals - Question 13
Save

In the figure, O is the centre of the circle. The measure of angle CBD is

Detailed Solution: Question 13

Test: Cyclic Quadrilaterals - Question 14
Save

ABCD is a cyclic quadrilateral in a circle with centre O. If angle ADC = 130°; then angle BAC is

Detailed Solution: Question 14

Test: Cyclic Quadrilaterals - Question 15
Save

ABC is an isosceles triangle in which AB = AC. If D and E are the mid points of AB and AC respectively, then the points D, B, C and E are

Detailed Solution: Question 15

5 docs|319 tests
Join Course
Information about Test: Cyclic Quadrilaterals Page
In this test you can find the Exam questions for Test: Cyclic Quadrilaterals solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Cyclic Quadrilaterals, EduRev gives you an ample number of Online tests for practice
Download as PDF
;

About this Class 9 Practice Test

This test contains 15 MCQs on Cyclic Quadrilaterals with detailed solutions for each question. It is part of the Online MCQ Tests for Class 9 course on EduRev, designed to align with the current Class 9 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

Explore more Class 9 Study Resources

If you found this Cyclic Quadrilaterals MCQ Test helpful, you can further enhance your Class 9 preparation with in-depth courses on EduRev, for all the subjects and topics available in Online MCQ Tests for Class 9 course. The course offers:
  • Video Lectures: covering all the topics of Online MCQ Tests for Class 9
  • Notes for Revision: offering revision notes, important questions, summaries, flashcards, cheatsheets & more for Class 9 preparation
  • MCQ Test: variety of questions as per the pattern of Class 9 exam
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup