​ A chord 10 cm long is drawn in a circle whose radius is 5√2 cm. Find area of both the segments.(Take π = 3.14) ​

Question

A chord 10 cm long is drawn in a circle whose radius is \(5\sqrt2\) cm. Find area of both the segments.(Take π = 3.14)

Answer 1

Length of chord = 10 cm 

Radius of circle = \(5\sqrt2\) cm

(This triangle POQ satisfy Pythagoras theorem) 

= PQ² = PO² + OQ² 

= 10² = (5\(\sqrt2^2\)) + (5\(\sqrt2^2\))

= 100 = 50 + 50 

So, 

Angle AOQ = 90° 

Area of sector = \(\frac{90}{360}π\times50\) = \(\frac{25}{2}π\) cm²

Area of triangle POQ = \(\frac{1}2\times5\sqrt2\times5\sqrt2\) = 25 cm²

Area of minor segment = \(\frac{25}{2}π - 25\)

= 14.25 cm²