Question

ΔDEF is formed by lines tangent to the circle, where = 13.7, = 9, and = 14. Determine the perimeter of ΔDEF.

Question 1 options:

1)

68.4

2)

73.4

3)

73.7

4)

73.1

Answer 1

Answer:73.4

Explanation:

Answer 2

Option (2)

Explanation:

To solve this question we will use the property of tangents drawn to a circle.

"Tangents drawn from an external point to a circle are equal in length"

From the figure attached,

In ΔDEF,

DA = DC = 14 units [Equal tangents]

EA = EB = 13.7 units [Equal tangents]

FB = FC = 9 units [Equal tangents]

Therefore, DE = DA + AE = 14 + 13.7 = 27.7 units

EF = EB + BF = 13.7 + 9 = 22.7 units

DF = DC + FC = 14 + 9 = 23 units

Perimeter of ΔDEF = DE + EF + DF

= 27.7 + 22.7 + 23

= 73.4 units

Option (2) will be the answer.