Question

In figure 3.94,
(1) m(arcCE) = 54°,m(arcBD) = 23°, find measure of ∠CAE
(2) If AB =4.2, BC=5.4,AE=12.0, find AD
(3) If AB=3.6, AC=9.0,AD=5.4, find AE

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

m(arcCE) = 54°,m(arcBD) = 23°, find measure of ∠CAE

let draw Δ OCE & Δ OBD

OC = OE = OB = OD = Radius

∠OEC = ∠OCE = (180° - 54°)/2 = 63°

∠OBD = ∠ODB = (180° - 23°)/2 = 78.5°

∠OCB = ∠OBC

∠OED = ∠ODE

∠CED + ∠CBD = 180°

∠OEC  + ∠OED + ∠OBD + ∠OBC = 180°

63° + ∠OED + 78.5° + ∠OBC = 180°

∠OED + ∠OCB = 38.5°   (∠OCB = ∠OBC)

∠AEC + ∠ACE + ∠CAE = 180°

∠OEC  + ∠OED + ∠OCE + ∠OCB + ∠CAE = 180°

=> 63° + (∠OED + ∠OCB) + 63° + ∠CAE = 180°

=> 38.5° + ∠CAE = 54°

=> ∠CAE =  15.5°

AB/AC = AD/AE

=> 4.2/(4.2 + 5.4)  = AD/12

=> 4.2/9.6 = AD/12

=> AD = 5.25

AB/AC = AD/AE

=> 3.6/9  = 5.4/AE

=> AE = 5.4* 9 /3.6

=> AE = 13.5