Question

A circle touches the aside EF of ∆DEF at P and touches sides DE and DF at Q and R resp. when produced. show that DQ=1/2 (perimeter of ∆DEF)​

Answer 1

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Answer 2

Given :- A circle touches the aside EF of ∆DEF at P and touches sides DE and DF at Q and R resp. when produced. show that DQ=1/2 (perimeter of ∆DEF) ?

Solution :-

we know that,

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

So,

• DQ = DR ----------(1)
• EQ = EP ----------(2)
• FR = FP --------- (3)

From diagram ,

→ DQ = DE + EQ

Putting value of EQ from (2),

→ DQ = DE + EP -------------- (4)

Similarly,

→ DQ = DR (From (1) )

→ DQ = DF + FR

Putting value of FR from (3) ,

→ DQ = DF + FP ------------- (5)

adding (4) and (5) we get,

→ DQ + DQ = (DE + EP) + (DF + FP)

→ 2DQ = DE + DF + (EP + FP)

→ 2DQ = DE + DF + EF

→ 2DQ = Perimeter of ∆DEF

→ DQ = (1/2)[Perimeter of ∆DEF] . (Proved).

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