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Geometry please help-
Find PQ

Geometry Please Help Find PQ class=

Sagot :

Devishri1977idn

Answer:

PQ = 29

Step-by-step explanation:

Lengths of the two tangents from a external point to the circle is equal

14x - 13 = 8x + 5  {add 13 to both sides}

    14x = 8x + 5 + 13

   14x  = 8x + 18

14x - 8x = 18

      6x =  18

       x = 18/6

x = 3

PQ = 14*3 - 13

      = 42 - 13

     =  29

Answer:

PQ = 29

Step-by-step explanation:

As we know that,

[tex]\star[/tex] Lengths of two tangents from a external point to the circle is equal.

[tex]\dashrightarrow\bf{14x - 13 = 8x + 5 \: .... \: (Adding \: 13 \: to \: both \: the \: sides)} \\ \\ \dashrightarrow\bf{14x = 8x + 5 + 13} \\ \\ \dashrightarrow\bf{14x = 8x + 18} \\ \\ \dashrightarrow\bf{14 - 8x = 18} \\ \\ \dashrightarrow\bf{6x = 18} \\ \\ \dashrightarrow\bf{\frac{\cancel{18}}{\cancel{6}}} \\ \\ \dashrightarrow\boxed{ \bf \red{x = 3}} \: \bigstar[/tex]

We've been asked to find out PQ;

[tex]:\implies\tt{PQ = 14x - 13} \\ \\ :\implies\tt{PQ = 14 \times (3) - 13} \\ \\ :\implies\tt{PQ = 42 - 13} \\ \\ \implies\boxed{ \tt\blue{PQ = 29}} \: \bigstar[/tex]

Thus,

  • The length of PQ is 29.
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