Geometry please help- Find PQ
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Answers
Answer:PQ = 29Step-by-step explanation:Lengths of the two tangents from a external point to the circle is equal14x - 13 = 8x + 5 {add 13 to both sides} 14x = 8x + 5 + 13 14x = 8x + 1814x - 8x = 18 6x = 18 x = 18/6x = 3PQ = 14*3 - 13 = 42 - 13 = 29
Answer:PQ = 29Step-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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