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[" (3) Tworight thingles "ABC" and "DBC"...

[" (3) Tworight thingles "ABC" and "DBC" are are are the same hypotenuse "B" cand on the same side of "R" ."],[" 32.If Acrighd "BD" intersect at "P" ,prove that "AP times PC=BP times DP" ."],[" "Fand "(tan theta)/(4000)+(c^(" cot "))/(" cot ")=1" (inen "]

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ABC and DBC are two right angled triangles with common hypotenuse BC with their sides AC and BD intersecting at P. Prove that: AP×PC=DP×PB .

Two triangle ABC and D B C lie on the same side of the base B C . From a point P on BC, PQ||AB and PR||BD are drawn. They meet A C in Q and D C in R respectively. Prove that QR||AD .

Two triangle ABC and D B C lie on the same side of the base B C . From a point P on B C ,P Q A B AND P R B D ARE DRAWN. They meet A C in Q and D C in R respectively. Prove that Q R A Ddot

Two perpendicular BD and CE are drawn from the vertices B and C respectively on the sides AC and AB of the Delta ABC ,which intersect each other at the point P. Prove that AC^(2) + BP^(2) = AB^(2) + CP^(2)

In squareABCD , side BC|| side AD . Digonals AC and BD intersect each other at P . If AP=(1)/(3)AC then prove DP=(1)/(2)BP .

In squareABCD , side BC|| side AD . Digonals AC and BD intersect each other at P . If AP=(1)/(3)AC then prove DP=(1)/(2)BP .

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

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

If in Delta ABC , angle C = 90 ^(@) prove that: ( 1+ tan A)/(1- cot B) xx (1- tan A)/(1+ cot B) =1.

If the sides a,b,c of a triangle ABC are in A.P., prove that cosA "cot" (A)/(2) , cosB "cot" (B)/(2), cosC "cot" (C)/(2) are also in A.P.