Answer :
Answer:
PR = 2
PQ + QR = PR, substitute values
5x - 4 + x = 2x, that is
6x - 4 = 2x ( subtract 2x from both sides )
4x - 4 = 0 ( add 4 to both sides )
4x = 4 ( divide both sides by 4 )
x = 1
PR = 2x = 2 × 1 = 2
The numerical length of PQ is 2 units.
What is the Angles of Intersecting Secants Theorem?
Angles of Intersecting Secants Theorem states that, If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.
Given data as :
PQ = x,
QR = 6,
And PR =2x - 10,
⇒ PQ + QR = PR,
Substitute values in the above equation,
⇒ 5x - 4 + x = 2x,
⇒ 6x - 4 = 2x
Subtract 2x from both sides,
⇒ 4x - 4 = 0
Add 4 to both sides,
⇒ 4x = 4
Divide both sides by 4
⇒ x = 1
⇒ PR = 2x
Substitute value in the above equation,
⇒ 2 × 1 = 2
Hence, the numerical length of PQ is 2 units.
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