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Given : Line ET is tangent to the circle...

Given `:` Line ET is tangent to the circle at point E. Line EAB is secant intersecting at point A and B.
To Prove ` : ET^(2) = EA xx EB `
Construction `:` Draw seg BT and Seg AT
Complete the proof by filling the boxes.

Text Solution

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In `Delta`EAT and `Delta ETB`,
`/_ AET ~= /_TEB ` ….`square `
`/_ ETA ~= /_EBT ` ….`square `
`:. Delta EAT ~ Delta ETB ` …`square `
`:. ( ET)/( square) = ( EA)/(square ) ` ….(Corresponding sides of similar triangle )
`:. EA xx EB = square `
Proof `:`
In `Delta EAT ` and `Delta ETB.`
`/_AET ~= TEB` ....Common angle
`/_ ETA ~= /_ EBT ` .....Tangent secant theorem
`:. Delta EAT ~ Delta ETB ` ....A A test of similarity
`:. (ET )/( EB ) = (EA )/( ET)` ....(Corresponding sides of similar triangle )
`:. EA xx EB = ET^(2)`
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