Question No.2 Let AB be a diameter of a circle with centre P and C be a point on AB such that 2AC = BC. Let D and Ebe points on the circle such that DC | AB and DE passes through P. If the area of AABD is 72 cm2 and that of ADCE is x cm2, then find x. (Note: Figure not to scale)
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Answer:
[ABD] [CDE] => 13.
Step-by-step explanation:
AB diameter of a circle
AC :CB=6:7
Let say AC = 6K
then CB = 7K
=> AB = AC + CB = 13K
DCLAB
[ABD] = Area of AABD
=> [ABD] = (1/2) AB * DC
=> [ABD] = (1/2) 13K * DC
DE the diameter Passing through Origin O
in ACDE CO is the median as it bisects DE,
=> [CDE] = 2 * [COD]
=>[COD] = (1/2)OC * CD
=> [CDE] = 2 * (1/2)OC* CD => [CDE] = OC * CD
AO = BO,
AC + OC = BC - OC
=> 6K + OC = 7K - OC
=> 20C = K
=> OC = K/2
=> [CDE] = K * CD/2
[ABD] / [CDE] = (1/2) 13K * DC/ (K* CD/2)
=> 13
[ABD] / [CDE] => 13. Answer
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