Vidaara.orgClass 9 · Mathematics
CodeVID-M09-10-CYC-01
Cyclic Quadrilaterals - Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
Opposite angles of a cyclic quadrilateral sum to:
- A.$90^\circ$
- B.$180^\circ$
- C.$270^\circ$
- D.$360^\circ$
2.
Through three non-collinear points passes exactly:
- A.no circle
- B.one circle
- C.two circles
- D.infinitely many
3.
The exterior angle of a cyclic quadrilateral equals the:
- A.adjacent angle
- B.interior opposite angle
- C.right angle
- D.central angle
4.
A quadrilateral is cyclic if its vertices lie on a:
- A.line
- B.circle
- C.triangle
- D.square
5.
If one angle of a cyclic quadrilateral is $80^\circ$, the opposite is:
- A.$80^\circ$
- B.$100^\circ$
- C.$90^\circ$
- D.$110^\circ$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
One angle of a cyclic quadrilateral is $70^\circ$. Find the opposite angle.
7.
How many circles pass through three non-collinear points?
8.
Opposite angles of a cyclic quadrilateral are $95^\circ$ and $x$. Find $x$.
9.
The exterior angle of a cyclic quadrilateral is $100^\circ$. Find the interior opposite angle.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
In cyclic quadrilateral $ABCD$, $\angle A=85^\circ$, $\angle B=95^\circ$. Find $\angle C$ and $\angle D$.
11.
Three angles of a cyclic quadrilateral (in order $A,B,C$) are $80^\circ,95^\circ,100^\circ$. Find the fourth.
12.
Can a circle pass through three collinear points?
13.
The exterior angle of a cyclic quadrilateral is $110^\circ$. Find the interior opposite angle.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
In cyclic quadrilateral $ABCD$, $\angle A=(2x+4)^\circ$ and $\angle C=(3x+1)^\circ$. Find $x$ and both angles.
15.
State the result about the opposite angles of a cyclic quadrilateral.
Answer Key
Section A — Multiple Choice Questions
- (B) $180^\circ$
- (B) one circle
- (B) interior opposite angle
- (B) circle
- (B) $100^\circ$
Section B — Short Answer (2 marks)
- $110^\circ$.
- One.
- $85^\circ$.
- $100^\circ$.
Section C — Short Answer (3 marks)
- $\angle C=95^\circ,\ \angle D=85^\circ$.
- $\angle D=85^\circ$.
- No.
- $110^\circ$.
Section D — Long Answer (5 marks)
- $x=35$; $\angle A=74^\circ,\ \angle C=106^\circ$.
- They are supplementary: $\angle A+\angle C=180^\circ$ and $\angle B+\angle D=180^\circ$.
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