Circle P is shown. Line segment P Q is a radius and has a length of 9. Line Q R is a tangent that intersects the circle at point
Q and has a length of 12. A line connects points R and P. The distance between point R and the circle is x, and the point on the circle to point P is a radius.
What value of x would make Line R Q tangent to circle P at point Q?
x =
What value of x would make Line R Q tangent to circle P at point Q?
x =
2 answers:
Answer:
X=6
Step-by-step explanation:
We need to remember the theorem that Tangent always makes a right angle at the point of contact with the circle.
Given details-
PQ=9= circle radius
QR=12
As given in the question
PQ is the radius
PQ=PY (since both are the radius to the circle)
⇒If the line QR = tangent than ∠ PQR must be 90°
Hence Δ PQR is a right-angled triangle with hypotenuse PR
PQ²+QR²=PR² (Pythagoras theorem)
∴Substituting the value of PQ, QR
⇒We get (9)² +(12)² = PR²
PR²= 225
⇒PR=15
As clear in figure PR= PY+YR
∴15=9+x
⇒ YR(x)= 6cm
You might be interested in