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 =

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  

what is all that apply?