Question

Geometry please help-
Find PQ

Answer 1

PQ = 29

Explanation:

As we know that,

`\star` Lengths of two tangents from a external point to the circle is equal.

`\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`

We've been asked to find out PQ;

`:\implies\tt{PQ = 14x - 13} \\ \\ :\implies\tt{PQ = 14 * (3) - 13} \\ \\ :\implies\tt{PQ = 42 - 13} \\ \\ \implies\boxed{ \tt\blue{PQ = 29}} \: \bigstar`

Thus,

• The length of PQ is 29.

Answer 2

PQ = 29

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