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In the given figure, O is the centre of the circle. The radius OP bisects a rectangle ABCD at right angles. DM = NC = 2 cm and AR = SB = 1 cm, KS = 4 cm and OP = 5 cm. What is the area of the rectangle? 

(a) 8 cm2 

(b) 10 cm2

(c) 12 cm2

(d) 16 cm2

1 Answer

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(b) 10 cm2.

OS = OP = ON = radii of the circle = 5 cm 

(OS)2 = (OK)2 + (KS)2 

⇒ 25 = (OK)2 + 16 

⇒ (OK)2 = 25 – 16 = 9 

⇒ OK = 3 cm 

LC = KB 

⇒ LN + NC = KS + SB 

⇒ LN + 2 = (4 + 1) cm ⇒ LN = 3 cm 

Similarly, (ON)2 = (OL)2 + (LN)2 ⇒ 25 

= (OL)2 + 9

⇒ (OL)2 = 16 ⇒ OL = 4 cm 

∴ LK = OL – OK = (4 – 3) cm = 1 cm 

Also, AB = DC = 10 cm 

∴ Area of rectangle ABCD = AB × BC = 10 cm × 1 cm = 10 cm2.

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