Answer:
The length of line segment QP is 20 units ⇒ 4th answer
Step-by-step explanation:
<em>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</em>
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
Given
R is the interior of ∠ TUV.
m∠ RUV=30degrees, m∠ TUV=3x+16, and m∠ TUR=x+10.
Find the value of x and the m ∠TUV.
To proof
As given in the question
m ∠TUV=3x+16, and m ∠TUR=x+10
thus
m∠ RUV = m∠ TUV - m∠ TUR
= 3x + 16 - x -10
= 2x + 6
As given
m ∠RUV=30°
compare both the values
we get
30 = 2x + 6
24 = 2x
12 = x
put this value in the m ∠TUV= 3x+16
m ∠TUV= 12× 3 +16
= 52°
Hence proved
