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Given: Circle k(O), O∈PLKE - tangent at EKE=18, PL=15 Find: KP
4 months ago
Q:
Given: Circle k(O), O∈PLKE - tangent at EKE=18, PL=15 Find: KP
Accepted Solution
A:
Answer:KP=12Step-by-step explanation:Use property for circle and tangent segment:tangent segment² = external secant segment · secant segment.In your case,tangent segment KE = 18;external secant segment KP;secant segment KL = KP + 15.Thus, 18²=KP(KP+15),KP²+15KP-324=0,D=15^2-4·(-324)=225+1296=1521,KP=(-15±39)/2=-27, 12.The segment cannot be of negative length, then KP=12.