A hoop is resting vertically at stair case as shown in the diagram.AB=12cm and BC=8cm. The radius of the hoop is..
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We have,
AB = 12 cm and BC = 8 cm
Let r be the radius of the hoop then,
OC = OA = r
We know that in rectangle JABC AB = JC = 12 cm& BC = AJ = 8 cm [opposite sides of rectangle are equal]
Now,
OJ = OA − AJ = (r − 8 ) cm
In right angled △ OJC
OC2 = OJ2 + JC2
⇒ r2 = (r − 8)2 + (12)2
⇒ r2 = r2 + 64 − 16r + 144
⇒ r2 = r2 + 208 − 16r
⇒ 16r = 208
⇒ r = 20816 = 13 cm
Hence, radius of the hoop is 13 cm.
(Check this attachment)
AB = 12 cm and BC = 8 cm
Let r be the radius of the hoop then,
OC = OA = r
We know that in rectangle JABC AB = JC = 12 cm& BC = AJ = 8 cm [opposite sides of rectangle are equal]
Now,
OJ = OA − AJ = (r − 8 ) cm
In right angled △ OJC
OC2 = OJ2 + JC2
⇒ r2 = (r − 8)2 + (12)2
⇒ r2 = r2 + 64 − 16r + 144
⇒ r2 = r2 + 208 − 16r
⇒ 16r = 208
⇒ r = 20816 = 13 cm
Hence, radius of the hoop is 13 cm.
(Check this attachment)
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