In the figure, AB and CD are parallel.

Prove that AP × PC = BP × PD

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Solution

Given: AB || CD

Construction: Draw XY parallel to AB such that it passes through point P.

We have AB || XY || CD

We know that three parallel lines cut any two lines in the same ratio.

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Similar questions

∠ B A C = ∠ B D C = 90^{\circ}

∠ A = ∠ C

In the figure AB and CD are extended to intersect at P. If AB = 5, BP = 3, PD = 2 then find CD.

(i) In the given figure, 3 $\times$ CP = PD = 9 cm and AP = 4.5 cm. Find BP.

(ii) In the given figure, 5 $\times$ PA = 3 $\times$ AB = 30 cm and PC = 4 cm. Find CD.

(iii) In the given figure, tangent PT = 12.5 cm and PA =10 cm; find AB.

B P \times P D = E P \times P C

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