Math, asked by lalipremlama2031, 3 months ago

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


madeducators2: post the picture please

Answers

Answered by amitnrw
43

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

brainly.in/question/2613154

If two equal chords of a circle intersect

brainly.in/question/8675681

Attachments:
Answered by jasminesaroya605
10

Answer:

the first answer is also right.

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