Question

A circle is inscribed in a ΔABC having sides
AB = 10 cm, BC = 12 cm and CA = 16 cm and
circle touches the sides AB, BC and AC of triangle
ABC at P, Q and R respectively. Find AP, BQ and
CR
Pls draw and give answer

Answer 1

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ANSWER

Given, a circle inscribed in △ABC, such that the circle touches the sides of the triangle.

Tangents drawn to a circle from an external point are equal.

∴AP=AR=7cm

CQ=CR=5cm

Now, BP=AB−AP=10−7=3cm

∴BP=BQ=3cm

∴BC=BQ+QC=3+5=8cm

∴ the length of BC is 8cm

Answer 2

Answer:

We know that

• AD= AF
• BD=BE
• CE=CF

Let AD=AF=x

• BD=BE=y

• CE=CF=z

Then x+y=12

y+z=8

x+z=10

On Solving above equation we get x=7,y=5,z=3

So AD=7 , BE=5 , CF= 3