Table of Contents
What are Circle Theorems?
There are a few different circle theorems that deal with specific aspects of circles. One such theorem is the inscribed angle theorem, which states that the measure of an angle inscribed in a circle is half the measure of the intercepted arc. Another theorem is the secant theorem, which states that the length of the secant from a point on a circle to the circumference is equal to the length of the chord drawn from the same point to the circle’s center.
All Theorems Related to Circle
There are several theorems related to circles that can be proved using basic algebra and geometry. Some of these theorems are:
- Theorem 1: The sum of the angles in a triangle is 180 degrees.
- Theorem 2: The sum of the radii of two circles is equal to the sum of their diameters.
- Theorem 3: The product of the radii of two circles is equal to the product of their diameters.
- Theorem 4: The area of a circle is equal to pi times the radius squared.
- Theorem 5: The circumference of a circle is equal to pi times the diameter.
Know Chord of a Circle
A chord of a circle is a line segment that connects two points on a circle. The length of the chord is the distance between the points.
Circles Class 9 Theorems
There are a few theorems that are specific to circles.
1. The Angle at the Center of a Circle is a Right Angle
2. The Radius of a Circle is Half the Distance from the Center to the Edge
3. The Area of a Circle is Pi*r^2
4. The Circumference of a Circle is Pi*d
All Theorems of Circle Class 9
Theorem 1:
A circle is the set of all points in a plane that are equidistant from a given point, called the center of the circle.
Theorem 2:
The length of the circumference of a circle is always the same.
Theorem 3:
The area of a circle is proportional to the square of the radius.
Solved Example
The following example illustrates how to find the equation of a line using the slope-intercept form.
The equation of a line with slope 3 and y-intercept (0, 2) is y = 3x + 2.
