Question

Seg ef is a diameter and seg df is a tangent segment. The radius of the circle is r. Prove thqt , DE ×GE =4r²

Answer 1

Answer:

Step-by-step explanation:

Line df is tangent and DE is secant

By tangent secant segment theorem,

DFx DF = DG x DE

In DFE

Angle f =90

By Pythagoras theorem,

De x de =df x df + ef x ef

De x de = df x df+4rxr

4rxr= de x de - df x df

4r x r = de x de-dg x de

4r x r =de (de - dg)

4rxr =de x ge