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A circle with centre P is inscribed in t...

A circle with centre P is inscribed in the ` Delta ABC` Side AB, side BC and side A C touch the circle at points L,M and N respectively . Prove that :
` A (DeltaABC ) = 1/2 (AB +BC + AC) xxr`

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Draw seg PA, seg PL , seg PN , seg PB , seg PC and seg PM
PL = Pm = PN = r …(radii of the same circle)
` PM bot BC, PL bot AB, PN bot AC " "` … (Tangent theorem )
` A ( Delta PBC) = 1/2 xxBC xx PM`
` :. A ( Delta PBC) = 1/2 xx BC xx r" "`... (1)
Similarly,
` A ( Delta APB ) = 1/2 xx AB xx r" "` ...(2)
` A ( Delta ABC) = A ( Delta PBC ) + A ( Delta APB) + A (Delta APC) `
..... (Area addition postulate )
` = 1/2 xx BC xx r + 1/2 xx AB xx r + 1/2 xx AC xx r " "` [ From (1), (2) and (3)]
` = 1/2 r (BC + AB +AC)`
` :. A ( Delta ABC) = 1/2 xx (AB+ BC + AC) xx r`
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NAVNEET PUBLICATION - MAHARASHTRA BOARD-CHALLENGING QUESTIONS-SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE ) Solve any one of the following subquestions :
  1. A circle with centre P is inscribed in the Delta ABC Side AB, side BC...

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  2. Solve any one of the following subquestions : Draw a circle with c...

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