(vii) In the given diagram, ∆ABC ~ ∆PQR and AD/PS = 3/8. (vi) The table shows the values of x and y, where x is proportional to y (v) Which of the following is/are an Arithmetic Progression (A.P.)? (iv) If the roots of equation 2 − 6 + = 0 are real and distinct, then value of k is: The sales are intra-state and the rate of GST is 10%. (iii) A retailer purchased an item for ₹1500 from a wholesaler and sells it to a customer at 10% profit. (ii) If 2 + + 6 = ( − 2 )( − 3) for all values of x, then the value of k is: Which of the following operation is possible? (Do not copy the question, write the correct answers only.) Students of Class X who are preparing for Board Exam 2024 can solved here Maths Sample Paper.Ĭhoose the correct answers to the questions from the given options. ICSE Board Class 10 Maths Sample Paper 2024 Solution New Sample Paper Solution ICSE Board 2024 Maths all Question Answers by Expert Teachers. The formula for finding out the arc length in radians has r as the radius of the circle and θ as the measure of the central angle in radians.ICSE Specimen Class 10 Maths Sample Paper 2024 Solution Every diameter is a chord, however not every chord can be a diameter.Īnswer: The arc of a circle refers to a portion of the circumference of a circle. Similarly, a chord that is passing through a circle’s centre point will be the diameter of the circle. Finally, just square the length of the chord.Īnswer: A chord of a circle refers to a straight line segment whose endpoints both lie on the circle. For example, if the height is three, we will multiply three times four to get twelve. We simply need to multiply the height of the chord times four. Question 3: How do you find the radius of a circle with a chord?Īnswer: It is easy to find the radius of a circle if the length and height of a chord of that circle are known. This term is taken from the Latin word “Chorda” that means “Bowstring“. In fact, it is also the longest chord possible in a circle. Diameter refers to the chord that passes through the centre of the circle. The endpoints of these line segments lie on the circle’s circumference. Therefore, ∠POQ = 2 x ∠PRQĪnswer: A Chord refers to a line segment that is joining any two points of the circle. Hence, ∠POQ is equal to two times of ∠PRQ. Question 1: In the following diagram, calculate the measure of ∠POQ when the value of ∠PRQ is given 62 0.Īnswer : According to the theorem of chords of a circle, the angle subtended at the center of the circle by an arc is twice the angle subtended by it at any other point on the circumference. Let us look at some solved examples based on these theorems. We will read about some other theorems in the next chapter. These are some of the basic theorems on the chords and arcs of a circle. This means that they all lie on the same circle. Theorem 10: If the line segment joining any two points subtends equal angles at two other points that are on the same side, they are concyclic. Theorem 9: Angles formed in the same segment of a circle are always equal in measure.ġ0. Theorem 8: The angle subtended by an arc at the center of a circle is double that of the angle that the arc subtends at any other given point on the circle.ĩ. It states that chords equidistant from the center of a circle are equal in length.Ĩ. Theorem 7: This is the converse of the previous theorem. Theorem 6: Equal chords of a circle are equidistant from the center of a circle.ħ. Theorem 5: If there are three non-collinear points, then there is just one circle that can pass through them.Ħ. In other words, any line from the center that bisects a chord is perpendicular to the chord.ĥ. Theorem 4: The line that is drawn through the center of the circle to the midpoint of the chords is perpendicular to it. It means that both the halves of the chords are equal in length.Ĥ. Theorem 3: A perpendicular dropped from the center of the circle to a chord bisects it. Cyclic Quadrilateral and Intersecting / Non-intersecting Circlesģ.It implies that if two chords subtend equal angles at the center, they are equal. Theorem 2: This is the converse of the previous theorem. Theorem 1: Equal chords of a circle subtend equal angles at the center.Ģ.Let us now look at the theorems related to chords of a circle.

You already know about the concepts of arc and circumference. T A Segment of the circle is the region that lies between the Chord and either of Arcs. Chord is derived from a Latin word “ Chorda” which means “ Bowstring“. It is the longest chord possible in a circle. Diameter is the Chord that passes through the center of the circle. The endpoints of this line segments lie on the circumference of the circle. A Chord is a line segment that joins any two points of the circle.

Equidistant chord geometry