Question

In a circle, the length of the chord (other than the diameter) is 2kcosθ and the perpendicular distance of the chord from the centre of the circle is ksinθ. Find the radius of the circle. (k is a positive real number)​

Answer 1

Theta is written as A

Step-by-step explanation:

Perpendicular from centre on chord, divides it into two equal parts.   Length of each part is  kcosA

In the formed triangle, using pythagoras theorem,

 ⇒ radius² = (kcosA)² + (ksinA)²

 ⇒ radius² = k²cos²A + k²sin²A

 ⇒ radius² = k²(cos²A + sin²A)

 ⇒ radius² = k²(1)

 ⇒ radius = k

Answer 2

Length of the chord ( other than the diameter ) = 2kcosθ

Half of chord = kcosθ

perpendicular distance of the chord from the center = ksinθ

We need to find radius , r of the circle .

Apply Pythagoras theorem ,

⇒ r² = (kcosθ)² + (ksinθ)²

⇒ r² = k²cos²θ + k²sin²θ

⇒ r² = k²(cos²θ + sin²θ)

⇒ r² = k²(1)

⇒ r² = k²

⇒ r = k

So , Radius of the circle = k units