Question

A circle is inscribed in triangle ABC. If AX = 5cm, cz = 9cm and
BY= 7cm, then find the perimeter of the triangle ABC.
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Answer 1

Step-by-step explanation:

We know that tangent drawn from external point to a circle are equal

So AD=AF=x

Or BD=BE=y

And CF=CE=z

Now, AB=AD+DB=x+y=12 cm ...(1)

Or BC=BE+EC=y+z=8 cm ...(2)

And AC=AF+CF=x+z=10 cm ...(3)

Adding the above three equation, we get

2(x+y+z)=12+8+10=30 cm

Or x+y+z=15 cm

As per equation (1),

x+y=12 cm

Then, z=15−10=5 cm =CF

As per equation (3),

x+z=12 cm

Then, y=15−12=3 cm =BE

As per equation (2),

y+z=8 cm

Then, x=15−8=7 cm =AD

Answer 2

Answer:

length of tangent from an external point is equal

AX= AZ =5cm

CZ= CY =9cm

BX= BY =4cm

AX + XB + BY + YC +CZ + ZA

5 +4 + 4 + 9+9+5

9+13 +14

22+14

36cm