In the given figure, D is the centre of the circle. if the length of the chords AB and BC are 12 cm and 16 cm respectively, find the radius of the circle.
Answers
Step-by-step explanation:
Given :-
In the given figure, D is the centre of the circle. if the length of the chords AB and BC are 12 cm and 16 cm respectively.
To find :-
Find the radius of the circle ?
Solution :-
Given that
D is the centre of the circle
A ,B, C are the points on the circle.
In ∆ ABC , angle B = 90°
Since ABC is a segment which is a semi circle
We know that
The angle in a semi circle is 90°
AC is the hypotenuse.
By Pythagorous Theorem ,
Hypotenuse² = Side²+Side²
=> AC² = AB²+BC²
=> AC² = 16²+12²
=> AC² = 256+144
=> AC² = 400
=> AC =√400
=> AC = 20 cm
Now,
Radius of the circle = AD = DC
But AC = AD+DC
=> AC = 2AD = 2DC
=> AD = DC = AC/2
=> AD = DC = 20/2
=> AD = DC = 10 cm
Therefore, Radius = 10 cm
Answer:-
Radius of the circle is 10 cm
Used formulae:-
Pythagoras Theorem:-
In a right angled triangle The square of the hypotenuse is equal to the sum of the squares of the other two sides.
- The perpendicular is drawn from the right angle to the opposite side then the perpendicular divides the side (hypotenuse) into two equal parts .
