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1.	From the diagram given below, angle subtended by the chord AB at the centre is __________(a) ∠OAB(b) ∠AOB(c) ∠ACB(d) ∠CABThis question was addressed to me in semester exam.I need to ask this question from Angle Subtended by a Chord at a Point in division Circles of Mathematics – Class 9
Answer» Right CHOICE is (b) ∠AOB Explanation: We can SEE from the diagram that “O” is the CENTRE of the CIRCLE, THEREFORE angle formed by the chord at the centre is ∠AOB.

2.	The region between an arc and the two radii, joining the centre to the end points of the arc is called __________(a) arc(b) chord(c) sector(d) area of circleI had been asked this question by my college director while I was bunking the class.This question is from Circles & its Related Terms in division Circles of Mathematics – Class 9
Answer» The correct OPTION is (C) sector The BEST EXPLANATION: The given STATEMENT is the definition of a sector. As we can see from the figure that there are two sectors, which are major sector and minor sector.

3.	From the diagram given below, if for two chords AB and CD, AB = CD, which of the following is true?(a) OM < ON(b) OM > ON(c) OM = ON(d) OM ≠ ONI got this question in my homework.Question is from Circles through Three Points in portion Circles of Mathematics – Class 9
Answer» RIGHT ANSWER is (c) OM = ON Explanation: According to theorem 10.6, EQUAL CHORDS of a circle are EQUIDISTANT from the centre. OM and on are the distance from the centre and chords AB = CD (given). Hence, OM = ON

4.	From the diagram given below, if for two chords AB and CD, AB = CD, which of the following is true?(a) OM < ON(b) OM > ON(c) OM = ON(d) OM ≠ ONThis question was addressed to me in class test.This interesting question is from Circles through Three Points in chapter Circles of Mathematics – Class 9
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5.	If a circle passes through three points which are collinear, the third point either lies outside or inside the circle.(a) True(b) FalseThis question was addressed to me in a national level competition.My query is from Circles through Three Points topic in section Circles of Mathematics – Class 9
Answer» The CORRECT option is (a) True The explanation: As shown in diagrams below, if a circle passes through three collinear points A, B and C, the THIRD point either lies outside the circle (FIGURE 1) or inside the circle (figure 2).

6.	How many circles can pass through three points which are not collinear?(a) One(b) Two(c) Three(d) FourI got this question during an online exam.Question is from Circles through Three Points topic in division Circles of Mathematics – Class 9
Answer» Right ANSWER is (a) ONE Best EXPLANATION: According to theorem 10.5, there is one and only one circle passing through three given non-collinear points. As can be seen in the DIAGRAM below, there can be only one circle through three non-collinear points A,B and C.

7.	When does both segments and both sectors become equal?(a) When two arcs are equal(b) When radius = 2 * chord(c) When two arcs are unequal(d) When chord = radiusI have been asked this question in a job interview.Query is from Circles & its Related Terms topic in chapter Circles of Mathematics – Class 9
Answer» RIGHT option is (a) When two arcs are equal To ELABORATE: As we can see in the DIAGRAM below, when two arcs are equal (when they are equal to semicircle), both SEGMENTS and both SECTORS are equal.

8.	From the diagram given below, what is the relation between ∠BAC and ∠BCD?(a) ∠BAD = ∠BCD(b) ∠BAD = 2∠BCD(c) ∠BAD = 0.5∠BCD(d) ∠BAD = 3∠BCDThe question was asked in a job interview.The above asked question is from Angle Subtended by an Arc of a Circle in division Circles of Mathematics – Class 9
Answer» Correct answer is (a) ∠BAD = ∠BCD The best EXPLANATION: ACCORDING to theorem 10.9, angles in the same SEGMENT are same. We can SEE that angles ∠BAC and ∠BCD are in the same segment and hence ∠BAD = ∠BCD.

9.	From the diagram given below, if ∠AOB is the angle subtended by an arc AB, then what is the relation between ∠AOB and ∠ACB?(a) ∠AOB = ∠ACB(b) ∠AOB = 2∠ACB(c) ∠AOB = 3∠ACB(d) ∠AOB = 0.5∠ACBThis question was addressed to me in examination.My doubt is from Angle Subtended by an Arc of a Circle topic in portion Circles of Mathematics – Class 9
Answer» Right answer is (B) ∠AOB = 2∠ACB Easiest explanation: According to theorem 10.8, 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.

10.	From the diagram given below, if lengths of the chords AB and PQ are equal, then ∠AOB = ∠POQ.(a) True(b) FalseI got this question in semester exam.My question comes from Angle Subtended by a Chord at a Point topic in division Circles of Mathematics – Class 9
Answer» Right choice is (a) True Best EXPLANATION: According to the theorem 10.1, EQUAL chords of a CIRCLE subtend equal ANGLES at the centre. Here, it is given that AB = PQ. Hence, ∠AOB = ∠POQ.

11.	The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called __________(a) square(b) triangle(c) rectangle(d) circleThe question was posed to me in an interview for internship.This intriguing question comes from Circles & its Related Terms in division Circles of Mathematics – Class 9
Answer» Correct OPTION is (d) circle The EXPLANATION: The given statement is the definition of the circle. “The collection of all the POINTS” is the circumferential of the circle and “fixed POINT” is the CENTRE.

12.	From the diagram given, arc ABC is major arc.(a) True(b) FalseI have been asked this question by my college director while I was bunking the class.I want to ask this question from Circles & its Related Terms in section Circles of Mathematics – Class 9
Answer» Right answer is (a) True Best explanation: As we can see in the diagram that ARC ABC is the longer ONE, therefore it is called major arc ABC. Similarly, smaller SIDE is called minor arc AC.

13.	From the diagram given below, if O is the centre of the circle and OL is perpendicular to chord AB, then which of the following is true?(a) AL > LB(b) AL < LB(c) AL ≠ LB(d) AL = LBThe question was asked during a job interview.This interesting question is from Angle Subtended by a Chord at a Point topic in chapter Circles of Mathematics – Class 9
Answer» CORRECT ANSWER is (d) AL = LB To explain: ACCORDING to theorem 10.2, perpendicular from the centre of a circle to a chord BISECTS the chord. Therefore, AL = LB.

14.	A circle divides the plane into __________ parts.(a) two(b) three(c) four(d) fiveI got this question by my college professor while I was bunking the class.This interesting question is from Circles & its Related Terms topic in division Circles of Mathematics – Class 9
Answer» Right option is (b) THREE The best I can explain: As shown in the diagram below, a circle DIVIDES the PLANE into three parts: 1) Interior, 2) Circle and 3) Exterior.