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In triangle A...

Question

In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that $Δ$ BPC is similar to $Δ$ ABC. Also, find the length of BP.

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Solution

In ∆ABC,
AB = AC = 8 cm
BC = 4cm
P is a point on AC such that AP = 6 cm
PB and PC are joined
To prove: ∆BPC ~ ∆ABC
and find length of BP
Proof: AC = 8 cm and AP = 6 cm
PC = AC – AP = 8 – 6 = 2 cm

$N o w space i n space triangle A B C space a n d space triangle B P C space fraction numerator A B over denominator B C end fraction space equals space 8 over 4 space equals space 2 a n d space i n space triangle B P C comma space fraction numerator B C over denominator C P end fraction space equals space 2 therefore space fraction numerator A B over denominator A C end fraction space equals space fraction numerator B C over denominator C P end fraction angle A B C space equals space angle C therefore increment A B C space tilde increment B P C therefore fraction numerator A C over denominator B P end fraction space equals 2 rightwards double arrow fraction numerator 8 over denominator B P end fraction space equals space 2 rightwards double arrow space B P space equals space 8 over 2 space equals space 4 c m$

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