In a circle of radius 5 cm, AB and AC are two chords such that AB AC6

1.	In a circle of radius 5 cm, AB and AC are two chords such that AB AC6 cm. Find the length of the chord BC.
Answer» See the diagram.we need to find 2y. In the right angled triangle AMC6² = x² + y²⇒ y² = 36-x² In the right angled triangle OMC5² = y² + (5-x)²⇒ 25 = (36-x²) + 25 + x² - 10x⇒ 25 = 36 - x²+ 25 + x² - 10x⇒ 0 = 36 - 10x⇒ x = 36/10 = 3.6 y =√(36-3.6²) =√23.04 = 4.8 cmBC = 2y = 4.8×2 = 9.6 cm

In a circle of radius 5 cm, AB and AC are two chords such that AB AC6 cm. Find the length of the chord BC.

Answer»

See the diagram.we need to find 2y.

In the right angled triangle AMC6² = x² + y²⇒ y² = 36-x²

In the right angled triangle OMC5² = y² + (5-x)²⇒ 25 = (36-x²) + 25 + x² - 10x⇒ 25 = 36 - x²+ 25 + x² - 10x⇒ 0 = 36 - 10x⇒ x = 36/10 = 3.6

y =√(36-3.6²) =√23.04 = 4.8 cmBC = 2y = 4.8×2 = 9.6 cm