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Three circle touch one another externally. The tangents at their points of contact meet at a point whose distance from the point of contant is 4. If the ratio of the product of the radii to the sum of the radii of the circle is `lambda,` then `lambda/2` is .........

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PATHFINDER-SOLUTION OF TRIANGLE AND HEIGHT AND DISTANCE-QUESTION BANK
  1. In a triangle ABC, right angled at A. The radius of the inscribed circ...

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  2. If in a DeltaABC, BC =5, CA=4, AB=3 and D, E are the point on BC such ...

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  3. Three circle touch one another externally. The tangents at their point...

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  4. If the radius of the circumcircle of a triangle is 12 and that of the ...

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  5. In a DeltaABC, the maximum value of 4((sumacos^2(A/2))/(a + b + c))mus...

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  6. The sides of a cyclic quadrilateral are in A.P., the shortest is 6 an...

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  7. In DeltaABC, r/r1=1/2, then the value of tan(A/2)(tan(B/2)+tan(C/2)) m...

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  8. In a triangle ABC, the incircle touches the sides BC, CA and AB at D,...

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  9. In triangle ABC, a=5,b=4,c=3. G is the centroid of triangle. If R1 b...

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  10. In the adjacent figure 'P' is any arbitrary interior point of the tria...

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  11. Prove that asin(B-C)+bsin(C-A)+csin(A-B)=0.

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  12. Prove that 1-tan(A/2)tan(B/2)=(2c)/(a+b+c).

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  13. Prove that acosA+bcosB+ccosC=2asinBsinC.

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  14. prove that cosA +cosB+cosC=1+r/R.

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  15. The sides of a triangle are x^2+3x+3,2x+3,x^2+2x. Find the greatest a...

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  16. If P1,P2,P3 be the altitudes of a triangle from the vertices A,B,C Res...

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  17. If in triangleABC ,a^4+b^4+c^4=2c^2(a^2+b^2) then find angleC

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  18. Let h1,h2,h3 be the altitudes of the DeltaABC and let the inradius be ...

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  19. For any triangle ABC, find the value of (bc cos^2(A/2)+cacos^2(B/2)+a...

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  20. If in a DeltaABC, sin^3A+sin^3B+sin^3C=3sinA.sinB.sinC,then find the v...

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