In the figure , AP || BQ || CR. Prove that ar `(DeltaAQC)` = ar `(DeltaPBR)` .

Triangle ABC and parallelogram ABEF are on the same base, AB as in between the same parallels AB and EF. Prove that ar (DeltaABC) = 1/2 ar(|| gm ABEF)

Let O be the circumcentre and H be the orthocentre of an acute angled triangle ABC. If A gt B gt C , then show that Ar (Delta BOH) = Ar (Delta AOH) + Ar (Delta COH)

ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB. Prove that (i) ar (ABCD) = ar(ABEF) (ii) ar (ABCD) = AB xx DG

In the figure, ABCD is a quadrilateral. AC is the diagonal and DE || AC and also DE meets BC produced at E. Show that ar(ABCD) = ar (DeltaABE).

PQRS and ABRS are parallelograms and X is any point on the side BR. Show that (i) ar(PQRS) = ar(ABRS) (ii) ar(DeltaAXS) =1/2 ar(PQRS)

In the figure seg AC and seg BD intersects each other at point P and (AP)/(CP)=(BP)/(DP) . Then Prove that DeltaABP~DeltaCDP .

In fig. if PQ||BC and PR||CD prove that (i) (AR)/(AD)=(AQ)/(AB) (ii) (QB)/(AQ)=(DR)/(AR) .

He, H , Ne , Ar

In the adjoining figure the circles with centers P and Q touch each other at R . A line passing through R meets the circles at A and B respectively then Prove that : (i) seg AP|| seg BQ. (ii) DeltaAPR~DeltaRQB . (iii) Find angleRQB if anglePAR = 35^(@)

In DeltaABC,APbotBC,BQbotAC,B-P-C,A-Q-C "then prove that " DeltaCPA~DeltaCQB. If AP = 7 , BQ = 8 , BC = 12 "then find" AC.