in a circle chord ab of length 6cm is at a distance of 4 cm from the centre O. the length of another chord CD.which is also 4 cm away from the centre is?
Answers
Answer:
6 cm
Step-by-step explanation:
By pythagoras theorem:-
(h)²=(4)²+(6/2)²=(4)²+(3)²=16+9
h=√25
h=5 cm
radius of the circle =5 cm
now, again
by pythagoras theorem,
(radius)²=(4)²+(cd/2)²
(5)²=(4)²+(cd)²/4
25-16=(cd)²/4
9×4=(cd)²
CD=√36
CD=6 cm
Given:
Length of chord AB = 6cm
The distance of AB from center O is 4cm
The distance of another chord CD from O is 4cm
To Find:
The length of chord CD
Solution:
Using the Pythagoras theorem we find the height of the triangle
(height)² = (base)² + (perpendicular)²
h² = b² + p²
Now, we substitute the values to find h
h² = (4)² + (6/2)²
h² = (4)² + (3)²
h² = 16 + 9
h² = 25
h = √25
h = 5
So, the height of the triangle is 5cm.
Now, again by using the Pythagoras theorem, we find the radius
r² = b² + p²
Then we substitute the following values
r² = (4)² + (CD/2)²
r² = (4)² + (CD)²/4
(6)² = (4)² + (CD)²/4
36-16 = (CD)²/4
20 = (CD)²/4
20/4 = (CD)²
5 = CD²
CD = √5
CD = 2.23
Therefore, the length of CD = √5