Question

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

Answer 1

Step-by-step explanation:

(a) Angle subtended by CD at O is 120° (Vertically opposite angles.

(b) Distance between A and C is

By PGT(Pythagorean theorem)

(AO)² = (AP)² + (PO)²

(13)² = (AP)+ 5²

169 - 25 = AP²

SO AP²= 144

AP = 12

SO, AC = 2(AP)

AC= 12×2

AC = 24

(c) ∠OCD = 30°

As ∠OCD=∠ODC ( because it is isocles triangle and OC = OD )

SO, ∠OCD+∠ODC+∠COD = 120

Let ∠OCD and ∠ODC be x,

So, x+x+120= 180 (Angle Sum Property)

2x=60

x= 30°

HOPE THIS HELPS...

Thank You..

Answer 2

Answer:

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