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[" Uswate case sample Question Papers,MATHEMATICS (Standard),Class-x "],[" 31.Two right triangles "ABC" and "DBC" are drawn on the same hypotenuse "BC" and on the same side of "BC" ."],[" If "AC" and "BD" intersect at "P" ,prove that "AP times PC=BP times DP" ."],[" ( "tan theta+(" cot "theta)/(1-tan theta)=1+sec theta" cosect "]

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Two triangles BACandBDC, right angled at Aand D respectively,are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P, prove that APxPC=DPxPB.

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 triangles, DeltaABC" and "DeltaDBC, lie on the same side of the base BC. From a point P on BC, PQ||AB" and "PR||BD are drawn. They intersect AC at Q DC at R. Prove that QR||AD.

Two triangles ABC and DBC are in the same side of the common base BC. Lines drawn parallel to BA and BD from any point E on BC intersect AC and DC at the points P and Q respectively. Show that PQ is parallel to AD.

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 .

Prove m:n theorem in a Delta ABC, a point D is taken on side BC such that BD:DC is m:n. Then prove that (1)(m+n)cot theta=m cot alpha-n cot beta(2)(m+n)cot theta=n cot B-m cot C

In a right triangle ABC right angled at B ,/_ACB=theta,AB=2cm and BC=1cm Find the value of sin^(2)theta+tan^(2)theta

Prove that: (1+sec 2theta)(1+sec2^(2)theta)(1+sec2^(3)theta)...... xx )(1+sec2^(n)theta) = tan2^(n)theta* cot theta