Answer:
NO = 3
Explanation:
Discussion
A secant is a line segment that intersects a circle in TWO places. If the secants start from the same point (O in this case) then the formula is
External Segment*Whole secant of one Secant = External segment*whole secant of the other secant.
Put into letters
NO(MN+NO) = OP*(OP + QP)
Givens
NO = ?
MN = 5
OP = 4
QP = 2
Solution
NO * ( 5 + NO) = 4(4+2)
5NO + NO^2 = 24 Subtract 24 from both sides
NO^2 + 5NO - 24 = 24-24 Combine
NO^2 + 5NOi - 24 = 0 Factor
(NO + 8)(NO -3) = 0
NO + 8 does not give a good answer. NO = - 8 which is not possible
NO - 3 = 0
NO = 3