Question

13. P is the centre of the circle of radius 20 cm. AB is a chord of the circle having it centre

at P. If AB = 32 cm, then find the distance of the chord AB from the centre P.​

Answer 1

Answer:

Step-by-step explanation:

Let's consider ΔOAD as RHS triangle,

OD (Distance between the Centre and radius of the circle) = ?

OA (Radius of the circle) = 16 cm

AD (1/2 of the chord AB) = 1/2×32 cm = 16 cm

As per Pythagoras theorem,

⇒ OD² + AD² = OA²

⇒ OD² + (16 cm)² = (20 cm)²

⇒ OD² + 256 cm² = 400 cm²

⇒ OD² = 400 cm² - 256 cm²

⇒ OD = √144 cm²  [The value of √144 cm² is 12cm]

⇒ OD = 12 cm

∴ The distance between the chord and the Centre of the circle is 12 cm.