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A circle is a closed plane geometric figure. The locus of a point moves around a fixed point at a fixed gap and that the outline is equidistant from the centre point.
Chapter circles of Class 10 help the students understand the concepts related to Circles and its properties. Circles is one of the important sections of geometry and questions related to it are asked not just in board exams but also in various competitive exams.
Class 10 students should solve RD Sharma for exposure to good questions on circles. The chapter is based on geometry and comes again in Class 12 Maths. That’s why the student must thoroughly be familiar with the fundamentals and should practice many questions.
A Circle is a round and closed figure, with all the boundary points lying equidistant from a fixed point, called the centre of a circle. The circumference of a circle is also called the perimeter of the circle as it is the total length of the boundary of a circle. The circumference of a circle is obtained by multiplying the constant π and the diameter of a circle. The circumference is one linear value and its units are the units of length.
2. What are some properties of a chord of a circle?
The chord of a circle is the line segment that joins any of the two points of the circumference of a circle. The diameter is also called the longest chord of the circle that passes through the centre of the circle. Some properties of the chord of a circle are:
The perpendicular to any chord, drawn from the centre of the circle, bisects it.
Chords of any circle that are equidistant from the centre of the circle are equal.
There is one and only one circle which can pass through 3 collinear points.
When a chord of a circle is drawn on it, it divides the circle into 2 regions of the major and minor area under them.
When a chord of a circle is extended to infinity on both sides, it becomes a secant
3. What is the major difference between a secant and a chord?
In a circle, when a secant line cuts the circle at 2 distinctive points, this results in a chord at the 2 points of intersection. The chord of the circle is a line segment with endpoints lying on the circular arc. It can be also described as, a chord is a line segment joining 2 distinctive points on the circumference of the circle, and if the particular chord is extended on both sides it becomes the secant of the circle. The secant line that passes through the centre of the circle is called the diameter of the circle.
4. What are the theorems of a secant of a circle?
In a circle, the secant is the line that intersects the circle at 2 distinct points. 2 secants can intersect either inside or the outside of a circle. The two theorems on properties of the secant of a circle are:
The angle formed by the two secants of a circle that intersect inside, is half the sum of the intercepted arcs.
The angle formed by the two secants of a circle, which intersect outside, is half the difference of the intercepted arcs.
5. What are some properties of the circle?
The common properties of a circle for class 12 students elaborately explained in the study materials provided by Vedantu are:
Area of the circle = πr2
Circumference of the circle= 2πr
Arc length of the sector of an angle A= (A/360) * 2πr
There is only and only 1 tangent at a point of the circle.
The point of contact is the common point of the tangent and the circle.
The line that contains the radius through the point of contact is also called the normal’ to the circle, at the given point.