Theorem 10.8 : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Text Solution
AI Generated Solution
To prove Theorem 10.8: "The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle," we can follow these steps:
### Step-by-Step Solution:
1. **Draw the Circle and Identify Points**:
- Draw a circle with center \( O \).
- Let \( P \) and \( Q \) be two points on the circumference of the circle, creating an arc \( PQ \).
- Choose any point \( A \) on the remaining part of the circle.
...
Topper's Solved these Questions
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 10.9|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 10.10|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 10.7|1 Videos
LINES AND ANGLES
NCERT ENGLISH|Exercise Exercise 6.1|6 Videos
NUMBER SYSTEMS
NCERT ENGLISH|Exercise EXERCISE 1.4|2 Videos
Similar Questions
Explore conceptually related problems
x-y+b=0 is a chord of the circle x^2 + y^2 = a^2 subtending an angle 60^0 in the major segment of the circle. Statement 1 : b/a = +- sqrt(2) . Statement 2 : The angle subtended by a chord of a circle at the centre is twice the angle subtended by it at any point on the circumference. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true
The total plane angle subtended by a circle at its centre is
The angle subtended by an arc of length 20 cm at the centre of circle when radius is 14 cm is
The angle subtended by the chord x +y=1 at the centre of the circle x^(2) +y^(2) =1 is :
Prove that any angle subtended by a minor arc in the alternate segment is acute and any angle subtended by a major arc in the alternate segment is obtuse.
The radius of a circle is 50 cm. Find the angle subtends by an arc of 22 cm length at the centerof the circle.
A chord of a circle is equal to the radius of the circle find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
A chord of a circle is equal to the radius of the circle find the angle subtended by the chord at a point on the monor arc and also at a point on the major arc.
A chord of a circle is equal to the radius of the circle find the angle subtended by the chord at a point on the monor arc and also at a point on the major arc.
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
