Question

A circle is inscribed in a triangle ABC touching bcca A B at P Q R respectively then find the length of BC ifab=10cm ,aq=7cmand cq=5cm

Answer 1

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Answer 2

Given :

A circle with center o inscribe in A Triangle ABC , and touches Triangle sides BC , AC , AB at P Q R  respectively

The length of side AB = 10 cm

The length of AQ = 7 cm

The length of QC = 5 cm

To Find :

The length of side BC

Solution :

From figure

As circle is inscribe in triangle, so sides of triangle acts as tangent touches the circle .

Now,

Length of PC = Length of QC       ( Tangents on same circle )

So, Length of PC = 5 cm .

Similarly

Length of AQ = Length of AR         ( Tangents on same circle )

So, Length of AR = 7 cm

∵  The length of AB = 10 cm

So,  Length of AR + Length of RB = length of AB

Or,  7  cm + Length of RB = 10 cm

∴     Length of RB = 10 cm - 7 cm

i.e   Length of RB = 3 cm

Again

Length of BP =Length of BR           ( Tangents on same circle )

So, length of BP = 3 cm

now,

Length of BC = Length of BP + Length of PC

i.e  Length of BC = 3 cm + 5 cm

∴   Length of BC = 8 cm

Hence, The Length of BC is 8 cm  . Answer