Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Facts that Matter: Circles
Facts that Matter: Circles | Mathematics (Maths) Class 10 PDF Download
Tangent to a Circle
A tangent to a circle is a line that touches the circle at only one point.
NOTE:
I. There is only one tangent at a point of the circle.
II. The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.
Theorem 1
The tangent at any point of a circle is perpendicular to the radius, through the point of contact.
Proof: We have the centre O of the given circle and XY is the tangent to the circle at a point P.
Let us take a point Q on XY other than P. Join OQ.
Obviously, Q lies outside the circle. i.e., OQ > OP
Since, all the points on XY, except P lies outside the circle.
i.e., OP is smaller than all the distance of the point O from XY.
i.e., OP is the smallest distance of O from XY.
i.e., OP ⊥ XY
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FAQs on Facts that Matter: Circles - Mathematics (Maths) Class 10
| 1. What are the properties of a circle? |  |
Ans. A circle has several properties, including:
- It is a closed curve made up of all points equidistant from a fixed point called the center.
- The distance from the center to any point on the circle is called the radius.
- The diameter is a line segment that passes through the center and has both its endpoints on the circle.
- The circumference is the distance around the circle and is calculated using the formula 2πr, where r is the radius.
| 2. How is the area of a circle calculated? | |
Ans. The area of a circle is calculated using the formula A = πr^2, where A represents the area and r represents the radius. In this formula, π is a mathematical constant approximately equal to 3.14159. To find the area, square the radius and multiply it by π.
| 3. How does the circumference of a circle relate to its diameter? | |
Ans. The circumference of a circle is directly related to its diameter. The ratio of the circumference to the diameter is always constant and equal to π (pi). In other words, the circumference of any circle is approximately 3.14159 times its diameter. This relationship is expressed in the formula C = πd, where C represents the circumference and d represents the diameter.
| 4. Can a circle have a negative radius? | |
Ans. No, a circle cannot have a negative radius. The radius of a circle represents the distance from the center to any point on the circle. Since distance cannot be negative, the radius must always be positive or zero. Negative values do not have any physical meaning when it comes to circle geometry.
| 5. Are all squares also circles? | |
Ans. No, all squares are not circles. A square is a quadrilateral with four equal sides and four right angles. On the other hand, a circle is a closed curve with all points equidistant from a fixed center. The two shapes have different properties, and while a square can be considered a regular polygon, it does not meet the criteria of a circle.
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