# Circle Geometry Math Problem Help? (diagram attached)?

A man designs a garden as shown. From point D outside the circle with centre C, two tangents, DA and DB, each 12 ft in length, meet the radius of the circle at points A and B respectively. Determine the total area of the man's garden.

### 3 Answers

- Mike GLv 76 months agoFavorite Answer
tan θ = 12/5

2θ = 134.76°

Central Reflex Angle = 360-134.76 = 225.24°

= 225.24π/180 radians

Area of circular part = 0.5*25*225.24π/180

= 49.14 ft^2

Area of the two triangles = 60 ft^2

Total Area = 109.14 ft^2

- PuzzlingLv 76 months ago
The area of the two triangle sections is easy to figure out. They are right triangles, so they each have an area of ½(5*12) = 30 ft² for a total of 60 ft².

So we just need the larger sector ACB.

Start by figuring out the angle θ using trigonometry:

tan θ = 12/5

θ = arctan(12/5)

θ = 67.38°

That means the central angle for the outside sector ACB is:

360° - 2θ

≈ 360° - 2 * 67.38°

≈ 225.24°

Now just take the full circle (π5² = 25π sq. ft.) and take the fraction for the sector.

Asector = (225.24 / 360) * 25π

Asector ≈ 39 sq. ft.

Add the 60 sq. ft. we previously calculated for the triangles.

Answer:

~99 sq. ft.

- Anonymous6 months ago
Do it yourself. We're not gonna do your fuсking homework for you.

I'm not sure where my calculator messed up. Maybe I copied 39 instead of 49. Anyway, the method was correct, sorry about the calculation mistake.