Latest iGate Aptitude Question SOLUTION: An isosceles triangle whose side are 13cm, 13cm, 10cm, is inscribed in a circle find the radius of circle

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An isosceles triangle whose side are 13cm, 13cm, 10cm, is inscribed in a circle find the radius of circle

Asked In iGate charan (11 years ago)

Solved RAKESH Read Solution (7)

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Read Solution (7) :

RAKESH  (11 years ago)

a=13,b=13,c=10

s =(a+b+c)/2 = (13+13+10)/2=18

area of triangle=[18(18-13)(18-13)(18-10)]^1/2 = (18*5*5*8)^(1/2) =60 cm^2

let R be the radius,then
R=(a*b*c)/(4*area of triangle)

R=(13*13*10)/(4*60)= 7.04cm

Is this solution Helpfull? Yes (16) | No (11)  

gayathri ramachandran  (10 years ago)

Let AB and AC be the equal sides and let BC be the base.
Now median AD drawn from vertex A to base BC bisects it into equal halfs.
So now apply pythagoras theorem on triangle ADC we get AD=12cm.
Now centroid divides median in the ratio 2:1 so upper half is
Radius of cicle which is,
2/3 *12 which is equal to 8 so ans is 8.

Is this solution Helpfull? Yes (13) | No (1)  

pramit  (9 years ago)

3.33...inradius=area of triangle/semiperimeter=60/18

Is this solution Helpfull? Yes (3) | No   

ABHOY KUMAR  (11 years ago)

AB=AC=13,CB=10, Let D be the mid point between C and B and also the perpendicular bisector of A. so, AD=rootunder((13^2)-(10^2))=AD=8.3. and perpendicular bisers of all points A,B,C coinside at the center of the circle also known as othocenter. and medians divides the median in the raio of 2:1. so radius of circle = (2/3)*8.3=5.537 cm(ANSWER)

Is this solution Helpfull? Yes (1) | No (8)  

RAGHAVENDRA M   (9 years ago)

P
* o *
* /| *
* / | *
* / |r *
/ | 13
* / | *
* / O* r *
* / | * *
/ | *
Q o- - - - o - - - -o R
* S 5 *
* *
* * *

In right triangle PSR=PS^2 + 5^2 =13^2 quadRightarrowquad PS = 12

. . Then: . OS =12-r


In right triangle OSR=OS^2 + SR^2 =OR^2 quadRightarrowquad (12-r)^2 + 5^2 =r^2

And we have: . 144 - 24t + r^2 + 25 =r^2 quadRightarrowquad -24r =169

. . Therefore: . r =169/24

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

Abir Das  (9 years ago)

s=(13+13+10)/2=18
area=√{18(18-13)(18-13)(18-10)}=60
let, height of the triangle is H
1/2 * 10 *H=60
=> H=12
As we know mid point of a circle divides height of triangle(inside the circle) in 2:1 ratio
hence, radius = 2/3 *12=8

Is this solution Helpfull? Yes (1) | No   

b.teja  (9 years ago)

ad2=ab2-bd2
ad=12
r=8

Is this solution Helpfull? Yes | No (1)  

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