Find the angle ADC and angle DAC

Asked by sunil_0010 | 9th Jan, 2010, 09:48: PM

Expert Answer:

 Dear Student

a=AB=4CM, b=BC= 3CM, c=CD=3.5CM, d=DA= 3.5CM

Radius of the circumCircle R= (1/4A)(ab+cd)(ac+bd)(ad+bc)

s=(a+b+c+d)/2 =7

Where A= (s-a)(s-b)(s-c)(s-d)= 12.124

==> R=(1/48.5)24.25X24.5X24.5  =2.4876

θ1, θ2, θ3, θ4  are tne angles between radius and chord a,b,c,and d respectively.

θ1= cos-1( a/2R)= cos-1(0.80)= 37

Similarly  θ2=cos-1( b/2R)=  53

θ3=cos-1( c/2R)=  45

θ4  =45

A= θ1=82

 B=θ12   =90

C= θ23  =98

D=θ34  =90

Regards

Topperlearning team 

 

Answered by  | 10th Jan, 2010, 01:28: PM

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