The shape of a park is a rectangle bounded by semi-circles at ends each of radius 7m as shown in figure. Find the perimeter of park.
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Let AB be a chord of a circle with radius 10 cm. OC ⊥ AB
∴ OA = 10 cm
OC = 5 cm
∵ OC divides AB into two equal parts
i.e. AC = CB
Now in right AOAC,
OA2 = OC2 + AC2 (Pythagoras Theorem)
⇒ (10)2 = (5)2 + AC2
⇒ 100 = 25 + AC2
⇒ AC2 = 100 – 25 = 75
∴ AC = 75−−√= 25×3−−−−−√ = 5 x 1.732
∴ AB = 2 x AC = 2 x 5 x 1.732 = 10 x 1.732 = 17.32
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