Question

in the circle chord cd is of 8cm length and chord ab is of 6cm length and they are 1cm apart from each other , what is diameter of circle?

Answer 1

The diameter is 48 cm.

Answer 2

Answer:

10 cm

Step-by-step explanation:

Since the distance between both the chord is 1 cm.

And the length of chord is 8 and 6 cm.

Construction: First draw the perpendicular line from the Chord to the center of the circle.

Thus, In ΔAOB,

r² = (8 ÷ 2)² + x²

⇒ r² = 16 + x²       → (1)

And In ΔCOD,

r² = (6 ÷ 2)² + (x + 1)²

⇒ r² = 9 + (x + 1)²        → (2)

From equation (1) and (2)

16 + x² = 9 + (x + 1)²

⇒ 16 - 9 = (x + 1)² - x²

⇒ 7 = x² + 1 + 2x - x²

⇒ 6 = 2x

⇒ x = 3

Putting the value of x in equation (1)

r² = 16 + (3)²

⇒ r² = 25

Thus, r = 5

And (Diameter) = 2 × (Radius)

(Diameter) = 2 × 5 = 10 cm