Answer:
The value of [tex]x=17 ft[/tex].
Step-by-step explanation:
Diagram of the given scenario shown below.
Given that,
Distance from bench to Jasmyn is [tex]PA=27ft[/tex].
Distance from bench to Willard is [tex]PB=(2x-7)ft[/tex].
From the Question,
The given wishing well is a circle and all the distance are tangent to the circle.
So, Triangle formed by these points are such as Δ[tex]PAO[/tex] and Δ[tex]PBO[/tex].
Now, taking both Δ[tex]PAO[/tex] and Δ[tex]PBO[/tex].
⇒ [tex]AO = BO[/tex] {Radius of circle are equal}
⇒ [tex]PO=PO[/tex] {Common side}
⇒ ∠[tex]PAO =[/tex] ∠[tex]PBO[/tex] {radius is always perpendicular
to the point of tangent }
∴ Δ[tex]PAO[/tex] ≅ Δ[tex]PBO[/tex] {By SAS congruence theorem}
Therefore, [tex]PA=PB[/tex] ....(1) {corresponding part of
congruence triangle (CPCT)}
Thus,
⇒ [tex]2x-7=27[/tex] {from equation (1)}
⇒ [tex]2x=34[/tex]
⇒ [tex]x=17 ft[/tex]
Hence, The value of [tex]x=17 ft[/tex].
