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Let P be the point inside that Delta ABC...

Let P be the point inside that `Delta ABC.` Such that `angle APB=angle BPC=angle CPA. ` Prove that
`PA+ PB +PC =sqrt((a^(2)+b^(2)+ c^(2))/(2)+ 2sqrt3Delta,)where a,b,c Delta` are the sides and the area of `Delta ABC.`

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ARIHANT MATHS ENGLISH-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Subjective Type Questions)
  1. In an obtuse angled triangle, the obtuse angle is (3pi)/4 and the othe...

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  2. If in triangle A B C a , b , ca n da ngl eA are given and csinA<a<c ,t...

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  3. If P is a point on the altitude AD of the triangle ABC such the /C B P...

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  4. If R denotes circumradius, then in DeltaABC,(b^2-c^2)/(2aR) is equal t...

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  5. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

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  6. If Delta = a^(2)-(b-c)^(2), Delta is the area of the Delta ABC then ta...

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  7. In a DeltaABC, B=90^(@), AC=h and the length of perpendicular from B t...

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  8. If in a Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C =3 sin A .Sin...

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  9. In a triangle ABC, if the sides a,b,c, are roots of x^3-11 x^2+38 x-40...

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  10. If the sides a,b,c are in A.P., prove that (tan)A/2+ (tan) c/2=2/3( co...

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  11. The sides of a triangle are in A.P. and its area is (3)/(5) th of an e...

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  12. If AD, BE and CF are the medians of a Delta ABC, then evaluate (AD^(2)...

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  13. Let AD be a median of the Delta ABC. If AE and AF are medians of the t...

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  14. In DeltaABC, If x= tan((B-C)/2) tan(A/2),y= tan((C-A)/2)tan(B/2), z=...

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  15. DeltaABC is equilateral triangle of side a. P lies on AB such that A i...

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  16. The base of a triangle is divided into three equal parts. If theta(1),...

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  17. If the circumradius of a triangle is 54/sqrt1463 and the sides are in...

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  18. If the angle at the vertex of an isosceles triangle having the maximum...

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  19. In an acute angle triangle ABC, AD, BE and CF are the altitudes, then ...

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  20. Let P be the point inside that Delta ABC. Such that angle APB=angle BP...

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