Question

The chord of circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is

(a) $\frac{5}{\sqrt{2}}$ (b) $5\sqrt{2}$ (c) $10\sqrt{2}$ (d) $10\sqrt{3}$

Answer 1

We know that cosθ=B⁄H (base/hypotenuse)

∴cos 45=OP⁄OA

OP=OA×cos45

OP=10×1⁄√2

∴length of chord= 2√(OA²-OP²)

= 2√(10²-10²⁄2)

= 2√(100-100⁄2)

= 2√(100-50)

= 2√(50)

= 2×7.07

= 14.14cm Ans