Question

Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT 

Answer 1

Given, radius = 13 units
PA = PB = 13 units
Using distance formula,
PT = `sqrt((-2 -2)^2  + (-4 + 7)^2)`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5
Using Pythagoras theorem in Δ PAT,
AT² = PA² - PT² 
AT² = 169 - 25
AT² = 144
AT = 12 units.