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Intercept Theorem

AB and CD are...

Question

AB and CD are parallel lines.

Then,

$A P \times P C$

$= (B P)^{2} \times (P D)^{2}$

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$A P \times P C$

$= (B P)^{2} \times P D$

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$A P \times P C$

$= \frac{B P}{P D}$

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$A P \times P C = B P \times B D$

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Solution

The correct option is D
$A P \times P C = B P \times B D$

Given, AB || CD

Draw another line parallel to AB through P.

So, $\frac{C P}{P B} = \frac{P D}{A P}$ (intercept theorem)

On, cross multiplication, $A P \times P C = B P \times P D$

Suggest Corrections

Similar questions

In the figure, AB and CD are parallel.

Prove that AP × PC = BP × PD

∠ B A C = ∠ B D C = 90^{\circ}

A B C D

A D ∥ B C

A C

B D

P

\frac{A P}{P D} = \frac{P C}{B P}

B E P

C P D

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

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

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