Question

Tangent Secant Theorem
Point E is in the exterior of a circle. A secant through E intersects the circle at points A and B, and a tangent through E touches the circle at point T, then `EA xx EB = ET^(2)`.
Given `:` (1) A circle with centre O
(2) Tangent ET touches the circle at pointT
(3) Secant EAB intersects the circle at points A and B .
To prove `:` `EA xx EB = ET^(2)`

Answer 1

Proof `:` In `Delta ETA` and `Delta EBT`,
`/_ AET ~= /_TEB ` …..(Common angle )
`/_ETA ~= /_EBT ` …(Tangent secant theorem )
`:. Delta ETA ~ Delta EBT ` …...(AA test of similarity )
`:. (ET)/( EB ) = (EA)/( ET )` ......(Corresponding sides of similar triangles are in proportion )
`:. EA xx EB = ET xx ET `
`:. EA xx EB = ET^(2)`