Geometry help needed Use O for exercises 6-8 6. what is the perimeter of triangle abc
1 answer:
Perimeter of triangle ABC is 20 units.
Solution:
The image for reference is attached below.
Given AE = 2, BD = 5 and CF = 3
Two tangents drawn from an external point to a circle are equal in length.
AD = AE, BF = BD and CE = CF
Therefore, AD = 2, BF = 5 and CE = 3
Perimeter of the triangle = sum of the three sides
Perimeter of triangle ABC = AB + BC + CA
= AD + BD + BF + CF + CE + AE
= 2 + 5 + 5 + 3 + 3 + 2
= 20
Hence, perimeter of triangle ABC is 20 units.
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A
using the Cosine rule in ΔSTU
let t = SU, s = TU and u = ST, then
t² = u² + s² - (2us cos T )
substitute the appropriate values into the formula
t² = 5² + 9² - (2 × 5 × 9 × cos68° )
= 25 + 81 - 90cos68°
= 106 - 33.71 = 72.29
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