Question

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Answer 1

Answer: 4

Explanation:

Given

PA=6, PD=4, BE=5

We know, If PEB is a secant that intersects the circle at E and B and PA be a tangent at A, then

`PA^2=PE\cdot PB`

Substitute the given values

`\Rightarrow 6^2=(PE+BE)\cdot(PE)\\\Rightarrow 36=(PE+5)\cdot(PE)`

Take
`PE=x`

`\Rightarrow 36=x^2+5x\\\Rightarrow x^2+5x-36=0\\\Rightarrow x^2+9x-5x-36=0\\\Rightarrow (x+9)(x-4)=0\\\Rightarrow x=-9,4`

Discard
`x=-9`

`\therefore PE=4`