Latest iGate Aptitude Question SOLUTION: An isosceles triangle those sides are 13cm,13cm,10cm long inscribed in a circle.find the radius of the circle.

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An isosceles triangle those sides are 13cm,13cm,10cm long inscribed in a circle.find the radius of the circle.

Asked In iGate Shalini (10 years ago)

Solved Shalini Read Solution (12)

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Read Solution (12) :

Shalini  (10 years ago)

a,b,c are sides of triangle ,ad is the median, ad^2=ab^2-bd^2 then ad=12,the centriod median divides into 2:1 ratio so 12 will be divide into 2:1 ratio so 8 is radius.
so ans is 8 cm

Is this solution Helpfull? Yes (15) | No (5)  

mathuku harani  (10 years ago)

above two answers are incorrect.7 is the 100% correct answer.if you want the brief explanation then send me a mail:harini.m104@gmail.com i will explain the answer

Is this solution Helpfull? Yes (4) | No (12)  

ASHWANI KUMAR  (9 years ago)

8 will be the answer coz in isoscelles triangle centroid orthocentre circumcentre all lie at a same point , so as we will get the ad= 12 cm and median divides the in the ratio 2:1 so the ans will be 8 .

Is this solution Helpfull? Yes (3) | No (1)  

Sravani A  (10 years ago)

a,b,c are vertex of tringle. the centriod median divides into 2:1 ratio so 12 will be divide into 2:1 ratio so 4 is the radius.

Is this solution Helpfull? Yes (2) | No (6)  

sreenivas reddy  (9 years ago)

isosceles tringle is inscribed in circle so circle>IS trianle
circumference of cirlce = 2*pi*r
circmuference of trianlge = 13+13+10=36

2*pi*r-36=0
2*pi*r=36
from this r=5.72 [where pi=22/7]

Is this solution Helpfull? Yes (2) | No (10)  

saikumar  (9 years ago)

13,13,10 so s=13+13+10/2=18
area of Triangle is =sqrt(18*3*3*10)=60
radius=(13*13*10)/(4*60)=7.04

Is this solution Helpfull? Yes (2) | No (1)  

priyanka madane  (8 years ago)

please someone explain it properly.....

Is this solution Helpfull? Yes (2) | No   

USHARANI  (8 years ago)

r=b/2*sqr((2a-b)/(2a+b))
a=13
b=10
c=13
so,the radius is 3.3333

Is this solution Helpfull? Yes (1) | No   

Gourav Kumar Pandey  (10 years ago)

Draw radii from center to the three intersections on the circumference
all having length r,
sine of half angle up at intersection of 13 cm legs = 5/13
so half angle = 22.6 degrees.

The Isosceles triangle now with legs r meeting base 13 at 22.6 angle.

=> cos 22.6 = r/6.5
=> r = 6.5 cos 22.6
=> r = 6

Is this solution Helpfull? Yes | No (9)  

pramit  (8 years ago)

3.33...as inradius=areaof triangle/semiperimeter=60/18

Is this solution Helpfull? Yes | No (2)  

Agalya  (8 years ago)

r=area of triangle/semiperimeter
sqrt(s(s-a)(s-b)(s-c))/s
s=a+b+c/2
3.33( 60/18)where s=18 aot=60

Is this solution Helpfull? Yes | No (3)  

Prashant  (8 years ago)

let sides are AB, BC (d is mid point), CA...(13, 10, 13)
find height of triangle is H=[ AB^2= Ad^2 + Bd^2]== [13^2=Ad^2 + 5^2]......... {10/2 = 5}
=> Ad=sqrt(169-25) = 12
internal circle radius of isosceles triangle is 1/3rd of height of ... 12/3===4....

answer is 4cm.

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