Question

In △MGN, MP⊥GN. If MG=a units, MN=b units, GP=c units and PN=d units.
Prove that (a+b)(a−b)=(c+d)(c−d).​

Answer 1

Explanation:

In ΔGMP,

Use Pythagoras Theorem,

a

2

=(MP)

2

+c

2

⟹a

2

−c

2

=(MP)

2

In ΔMNP,

Use Pythagoras Theorem,

b

2

=(MP)

2

+d

2

⟹b

2

−d

2

=(MP)

2

Equating both,

a

2

−c

2

=b

2

−d

2

⟹a

2

−b

2

=c

2

−d

2

⟹(a−b)(a+b)=(c−d)(c+d)

⟹

(c−d)

(a−b)

=

(a+b)

(c+d)

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