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Term 2 Assignment
NSC
3.2 In the diagram, DE is a tangent to the circle at \( \mathrm{E} \) and \( \mathrm{DFG} \) is a secant intersecting the circle at \( \mathrm{F} \) and \( \mathrm{G} . \mathrm{DE}=\mathrm{EF}=\mathrm{FG} . \mathrm{H} \) is a point on \( \mathrm{EG} \) such that \( \mathrm{FH} \| \mathrm{DE} \).
3.2.1 Determine, giving reasons, 3 angles each equal to \( D \hat{E} F \).
3.2.2 Prove that:
a) \( \triangle \mathrm{DEF}|| \mid \triangle \mathrm{DGE} \)
b) \( \hat{\mathrm{D}}=72^{\circ} \).
3.2.3 If it is further given that \( \mathrm{DF}=k \) units and \( \mathrm{FG}=2 \) units, prove that \( k^{2}+2 k=4 \).
3.2.4 Determine, giving reasons, the ratio of \( \frac{\mathrm{GH}}{\mathrm{GE}} \) in terms of \( k \).
TOTAL MARKS: 50
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