what is the length of line segment pq? 4 units 5 units 6 units 9 units
what is the length of line segment pq? 4 units 5 units 6 units 9 units
Answer
Explanation:
Step1: Apply tangent - secant rule
If (MN) is a tangent and (PN) is a secant to the circle, then (MN^{2}=NQ\times NP). Let (PQ = x), so (NP=x + 4). Given (MN = 6) and (NQ=4). We have the equation (6^{2}=4\times(x + 4)).
Step2: Solve the equation
First, expand the right - hand side: (36=4x+16). Then subtract 16 from both sides: (4x=36 - 16=20). Divide both sides by 4: (x = 5).
Answer:
5 units