A farmer has a circular garden as shown in the picture, which
has different types of trees, plants and flowers. 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 120o
at the centre O and AC is at a
distance of 5m from the centre. The radius of the circle is 13m.
(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
Answers
Given : 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
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If two equal chords of a circle intersect
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