Question

let AB be a diameter of a circle and let c be a point on the segment AB such that AC :CB=6:7 ratio . Let D be a point on the circle such that DC is perpendicular to AB . let DE be the diameter through . If [XYZ ] denotes the area of the triangle XYZ, find [ABD]/[CDE] to the nearest integer.
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Answer 1

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

DC⊥AB

[ABD] = Area of ΔABD

=>  [ABD]  = (1/2) AB * DC

=>   [ABD]  = (1/2) 13K * DC

DE the diameter  Passing through Origin O

in ΔCDE  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

=> 2OC = K

=> OC = K/2

=>  [CDE] = K * CD/2

[ABD]  /   [CDE]  = (1/2) 13K * DC / ( K * CD/2)

= 13

[ABD]  /   [CDE]  =  13