Question

Find the perimeter of DEFG

Answer 1

Hint:
Here, we are asked to find the perimeter of DEFG. First, we will compare the adjacent sides from the figure. Now, to find the perimeter we will add all adjacent sides. Thus, we will get the perimeter of DEFG.

Complete step by step solution:
Here we Know that lengths of tangents from the external point to the circle are equal. Observe that Points D, E, F, D are working as external points Also DR, DQ, are tangents from D to circle, ER, ES are tangents from E to circle, FP, FS are tangents from F to circle and GP, GQ are tangents from G to circle. SO these lengths will be equal.
So, we get
 \[\begin{array}{*{20}{l}}
  {QD = DR = 4} \\
  {ER = ES = 5} \\
  {SF = FP = 7} \\
  {GP = GQ = 5}
\end{array}\]
Now, we have to find the perimeter,
Perimeter = Sum of all sides
=EF + FG + GD + DE
 \[ = \left( {5 + 7} \right) + \left( {7 + 5} \right) + \left( {5 + 4} \right) + \left( {4 + 5} \right)\]
$= 12 + 12 + 9 + 9 \\
=24 + 18 \\
=42 cm$

Hence, the perimeter of DEFG is 42 cm.

Note:
Perimeter: A perimeter is a path that surrounds a two-dimensional shape. The term may be used either for the path, or its length-in one dimension. It can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference.