CASE STUDY 2. A farmer has a circular garden as shown in the picture below. He has different type of trees, plants and flower plants in his garden. In the garden there are two Mango trees A and B at a distance of AB=10m. Similarly he has two Ashoka trees at the same distance of 10m as shown C and D.AB subtends angle AOB =120 at the centre O, the perpendicular distance of AC from centre is 5m. The radius of the circle is 13m. Answer the following questions: i. What is the value of angle COD?
Answers
Answer:
In the garden there are two mango trees A and B such that AB = 10m. Similarly there are two ashoka trees C and D at the same distance 10m
AB subtends 120° at the centre O
AC is at a distance of 5m from the centre
The radius of the circle is 13m
To Find : (a) What is the angle subtended by CD at the centre O?
(b) What is the distance between mango tree A and ashoka tree C?
(c) Find ∠OCD
Solution:
Equal chords subtends equal angle at center
Chord AB = Chord CD = 10 m
Hence angle subtended by CD at the centre O = angle subtended by AB at the centre O
=> angle subtended by CD at the centre O = 120°
Distance between A & C
= 2 ( √(13² - 5²)
= 2( 12)
= 24 m
∠OCD = ∠ODC as OC = OD
=> ∠OCD + ∠ODC + ∠COD = 180°
=> 2∠OCD + 120° = 180°
=> ∠OCD = 30°
∠ODC = 30°
Similarly ∠OAB = 30°
Note : Chord 10 m will make only around 45 deg angle at center ( not 120°)
but we have solved it as per given value 120° only
Learn More :
Prove that equal chords of circle subtend equal angles at the centre
brainly.in/question/2613154
If two equal chords of a circle intersect
Step-by-step explanation: