Latest TCS Aptitude Question SOLUTION: A semicircle is drawn with AB as its diameter . From c, a point on AB, a line perpendicular to AB is drawn , meeting the circumference of the semicircle at D. Given that AC=2 cm, C

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A semicircle is drawn with AB as its diameter . From c, a point on AB, a line perpendicular to AB is drawn , meeting the circumference of the semicircle at D. Given that AC=2 cm, CD= 6cm, the are of the semicircle ( in sq. cm ) will be:
1. 82pi
2. 50pi
3. 31pi
4. 55pi

Asked In TCS harshit gupta (9 years ago)

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ANKIT JAISWAL  (9 years ago)

2. 50 pi is the answer
Let O be the centre of semicirle. Draw the figure as per the question and join OD, n let OD=x.
then OD=OA=x radius of the semicircle
AC=2, so oc= x-2
Now in triangle OCD
CD=6, OD=x, OC=x-2,
solving OD^2=OC^2+CD^2
we get x=10
so area will b 100pi/2=50pi ;) :p

Is this solution Helpfull? Yes (15) | No   

Anuj Yadav  (9 years ago)

In triangle ACD
angle ACD is of 90
Let angle A=theta
this implies tan(90-theta)=AC/CD ......(1)

In triangle ADB
angle D is of 90
Hence angle B will be 90-theta(as angle A is theta we assumed)

In triangle BCD
angle C is of 90
angle B is 90-theta
therefor tan(90-theta)=CD/CB .....(2)


Solvind 1 and 2
AC/CD=CD/CB
CB=18cm

hence Diameter of circle that is AB=20cm

=>radius=10
area of semicirle=100pi/2
=50pi


Hence answer is 50pi
option 2 is correct


Correct me if I am Wrong

Is this solution Helpfull? Yes (14) | No (1)  

Shachi  (9 years ago)

AC=2
CD=6
SO accordingly the hypotenus with centre and D is radius hit and trial radius can be 10
so area =50pi

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