Question

In figure 3. 81 , seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DF * GE = 4r

Answer 1

proof :-
DF is a tangent and EF is a secant.
by tangent secant segment theorem.
•
• • DF* =DExDG....... (1)
HF perpendicular to EF......( tang. theorem)
ΔDEF is a right angled triangle.
•
• •DE*=DF* ➕ EF*
DE* =DF* ➕ ((2r*)
DE* ➖ DF*= 4r*
DE* ➖ DE ✖ DG=4r*
DF(DE ➖ DG) =4r*
DF ✖ GE=4r*







*=
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