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.
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Class 10 Circles learning videos
Work through Circles with these lessons.
LEARN BY DOING
Free Circles Olympiad Questions for Class 10
5 questions to build confidence. Choose an answer, then explore the explanation.
01
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)?
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Answer: C. The volume is larger by a factor of 1.5.
With the same radius, volume is proportional to height. 15/10 = 1.5.
02
The apothem of a regular polygon is perpendicular to one of its sides.
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The answer key for this sample question is not available yet.
03
Given that P(A) = 0.71, P(B) = 0.22, and P(A|B) = 0.13, what is P(A and B)?
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Answer: A. 0.03
P(A and B) = P(A|B)P(B) = 0.13 × 0.22 = 0.0286 ≈ 0.03.
04
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.
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Answer: A. 12,137 mph
4,500 gallons/hour means 9 thrusters, so speed = 3000(1.15)^8 ≈ 12,137 mph.
05
What is the definition of supplementary angles?
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The answer key for this sample question is not available yet.