Answer:
The length of line segment QP is 20 units ⇒ 4th answer
Step-by-step explanation:
If a secant and a tangent are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment
Look to the attached figure
∵ PQ is a tangent to the circle
∵ PM is a secant intersects the circle at points N and M
- That means the product of the lengths of PM and PN is
equal to the square of the length of PQ
∴ (PQ)² = (PN). (PM)
∵ The length of Q P is n units
∴ PQ = n
∵ The length of N P is 11.5 units
∴ NP 11.5
∵ The length of M N is 24 units
∴ MN = 24
- The length of the secant PM is the sum of the lengths of PN
and MN
∵ PM = PN+ NM
∴ PM = 11.5 + 24 = 35.5
Substitute the values of PQ, PN, and PM in the formula above
∵ n² = 11.5 × 35.5
∴ n² = 408.25
- Take √ for both sides
∴ n = 20.205197
- Round it to the nearest unit
∴ n = 20
∵ n is the length of PQ
∴ The length of line segment QP is 20 units
