Learn Class 10 Math - Circles

The circle is a term that has three possibilities, including the non-intersecting point, single common point, or two common points. In the single common point, the line will touch the circle, whereas the line will cut the circle in the two common points.

Components of the Circle

The circle has different components, and these components are discussed below:

  • Tangent

    Tangents are lines in circles that connect one point on the circle to another point at the same time. Each point lies on a different tangent.

  • Secant

    The secant of the circle has two points in common with the circle. The secant will cut the circle at two points. And it will form the chord of a circle.

  • Radius

    Radius is the distance from the circle that remains constant.

  • Diameter

    Basically, the diameter is the entire length that passes through a circle.

  • Chord

    The line that joins any two circle points is known as a chord.

Properties of a Circle

Evaluate that the tangent of the circle is perpendicular to the radius of a circle.

It is given that AB is the tangent of the circle at point Q. O is the centre.

We have to prove that OQ ⊥ AB.

Solution:

Take a point P on AB and join it.

If point p lies in the circle, then AB will be a secant.

OP > OQ.

Learning Videos for 10th Grade Math - Circles

Circles Sample Questions for Class 10

Question 1

The volume of a cone is given by the expression 1/3 pi r^2 h, where r is the radius of the cone and h is the height of the cone. If one cone has a height of 10 cm, and a second cone has a height of 15 cm, how much larger is the volume of the second cone (assuming the radius is the same in each cone)?
A. The volume is 5 \ "cm"^3 larger.
B. The volume is larger by a factor of 9/4.
C. The volume is larger by a factor of 1.5.
D. This cannot be determined without knowing the radius.

Question 2

The apothem of a regular polygon is perpendicular to one of its sides.
A. True
B. False

Question 3

Given that P(A) = 0.71, P(B) = 0.22, and P(A|B) = 0.13, what is P(A and B)?
A. 0.03
B. 0.04
C. 0.09
D. 0.42

Question 4

A new spaceship has been developed. It has many small rocket thrusters that can be used together. If just one thruster is used, the ship travels at a speed of 3,000 miles per hour. Each additional thruster causes the ship to travel 15% faster. However, each thruster uses 500 gallons of fuel per hour. About how fast is the spaceship traveling if it is using 4,500 gallons of fuel per hour? Round answers to the nearest mile per hour.
A. 12,137 mph
B. 7,980 mph
C. 10,554 mph
D. 9,177 mph

Question 5

What is the definition of supplementary angles?
A. Two angles that add to be 180 deg
B. Two angles that have a difference of 90 deg
C. Two angles add to be 90 deg
D. Two angles that have a difference of 180 deg