Question

radius of a cirlcle is 13cm and the length of one of its chords is 10 cm.find the distance of chord from the centre​

Answer 1

Given :

• Radius of the circle (AO) = 13 cm
• Length of one of its chord (AB) = 10 cm

To find :

• Distance of the chord from the centre (OP)

Solution :

AB = 10 cm

2AP = AB

→ AP = AB/2

→ AP = 10/2

→ AP = 5 cm (∵ Perpendicular from the centre bisects the chord.)

In ∆AOP

By using pythagoras theorem,

→ H² = P² + B²

where,

• H = Hypotenuse (Longest side)
• P = Perpendicular
• B = Base

Hypotenuse = AO

Perpendicular = OP

Base = AP

⠀⠀⠀⇒ (AO)² = (OP)² + (AP)²

⠀⠀⠀⇒ (13)² = OP² + (5)²

⠀⠀⠀⇒ (13)² - (5)² = OP²

By using algebraic identity,

• (a + b)(a - b) = a² - b²

⠀⠀⠀⇒ (13 - 5)(13 + 5) = OP²

⠀⠀⠀⇒ (8)(18) = OP²

⠀⠀⠀⇒ 144 = OP²

Taking square root on both the sides,

⠀⠀⠀⇒ √144 = OP

⠀⠀⠀⇒ ± 12 Reject - ve = OP

⠀⠀⠀⇒ 12 = OP

∴ Distance of the chord from the centre (OP) = 12 cm