Question

. In the given figure, O is the centre of the circle. Determine APC, if DA and DC are tangents and
ADC = 50°.
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Answer 1

Answer:

Step-by-step explanation:

Age of A is 20 years less than the age of B.

i.e., A + 20 = B ______(i)

Age of B is thrice the age of C.

i.e., B = 3C ______(ii)

Age of C is half the age of D.

i.e., 2C = D ______(iii)

Age of D is 38 years.

i.e., D = 38 ______(iv)

To Find:

What is the age of B?

First finding the age of C:

In equation (iii).

⟶ 2C = D

Substituting the value of D from eqⁿ (iv).

⟶ 2C = 38

⟶ C = 38/2

⟶ C = 19

∴ Age of C = 19 years

Now finding the age of B:

In equation (ii).

⟶ B = 3C

Substituting the value of C.

⟶ B = 3 × 19

⟶ B = 57

∴ Age of B = 57 years

Finding the age of A:

In equation (i).

⟶ A + 20 = B

Substituting the value of B.

⟶ A + 20 = 57

⟶ A = 57 - 20

⟶ A = 37

∴ Age of A = 37 years.