> = 1.25 EXAMPLE 37 Two triangles BAC and BDC, right angled at A and Drespectively, are drawn on the some base BC and on the same side of BC. If AC and DB intersect at P, prove that AP x PC=DPxPB. (CBSE 2000C, 2019) ARR and APPC. We have

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.

Two triangles B A Ca n dB D C , right angled at Aa n dD respectively, are drawn on the same base B C and on the same side of B C . If A C and D B intersect at P , prove that A P*P C=D P*P Bdot

Two triangles QPR and QSR, right angled at P and S respectively are drawn on the same base QR and on the same side of QR. If PR and SQ intersect at T, prove that PT xx TR= ST xx TQ .

triangleBAC and triangleBDC are two right-triangle on the same side of the base BC.If AC ans DB intersect each other at a point P,show that APxxPC=DPxxPB .

Triangles ABC and DBC are two isosceles triangles on the same base BC and their vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that: AP bisects angle BAC and BDC.

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.

triangleABC and triangleDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that: (i) triangleABD ~= triangleACD (ii) triangleABP ~= triangleACP (iii) AP bisects angleA as well as angleD (iv) AP is the perpendicular bisector of BC.

DeltaABC and DeltaDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (See Fig. ).If AD is extended to intersect BC at P, show that AP bisects angleA as well as angleD .