Match the following with its correct value of PA

6cm

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10cm

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4cm

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Solution

$P D \times P C = P A \times P B$
$6 \times 25 = 15 \times P A$
$P A = 10 c m$

$P C \times P D = P B \times P A$
$7 \times 12 = 14 \times P A$
$P A = 6 c m$

$P T^{2} = P A \times P B$
$6^{2} = P A \times (P A + 5)$
$36 = (P A)^{2} + 5 P A)$
Let
PA be x
So,
$36 = x^{2} + 5 x)$
$x^{2} + 5 x - 36 = 0$
$(x + 9) (x - 4)$
x= -9,4
So, x=4cm { as the value of PA can not be negative }

$P A = 4 c m$

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