Question

In figure, LM || BA, LN || CA and PL = 10 cm. Find PB x PC.
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Answer 1

Step-by-step explanation:

In △ABC,

In △ABC,LM∥BC

In △ABC,LM∥BC∴ By proportionality theorem,

In △ABC,LM∥BC∴ By proportionality theorem,AB

In △ABC,LM∥BC∴ By proportionality theorem,ABAM

In △ABC,LM∥BC∴ By proportionality theorem,ABAM

In △ABC,LM∥BC∴ By proportionality theorem,ABAM =

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = AC

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,AD

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN =

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = AC

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)∴ from (1) and (2),

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)∴ from (1) and (2),AB

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)∴ from (1) and (2),ABAM

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)∴ from (1) and (2),ABAM

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)∴ from (1) and (2),ABAM =

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)∴ from (1) and (2),ABAM = AD

In △ABC,LM∥BC∴ By proportionality theorem,ABAM = ACAL ............(1)Similarly,In △ADC,LN∥CD∴ By proportionality theorem,ADAN = ACAL ............(2)∴ from (1) and (2),ABAM = ADAN

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Answer 2

Answer:

Step-by-step explanation:

Tip: prove similarity in ∆PCM and ∆PLN

solution: in ∆ PCM,

NL||MC, (by BPT)

PL/LC = PN/NM ----- (1)

in∆PLN, (by BPT)

BN||LM

PB/BL = PN/NM ------ (2)

from (1) and (2)

we can say that

PL/LC = PB/BL

. (Or)

LC/PL +1 = BL/PB +1

PC/PL = PL/PB

PC×PB = PL×PL

(given, PL=10cm)

therefore, PC×PB = 100