Question

The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.

• A. 5 cm
• B. 30 cm
• C. 20 cm
• D. 10 cm

Answer 1

The correct option is B

30 cm

A circle with centre O.

Radius of the circle = 17 cm

AB is chord and OM $\perp$ AB which bisects it at M

In right $\Delta OAM$,

$\Rightarrow O{A}^2=A{M}^2+O{M}^2$

$\Rightarrow (17{)}^2=A{M}^2+(8{)}^2$

$\Rightarrow 289=A{M}^2+64$

$\Rightarrow A{M}^2=289-64=225=(15{)}^2$

$\therefore$ AM = 15 cm

Hence AB = 2AM = 2 $\times$ 15 = 30 cm