Question

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 =

Answer 1

X=6

Explanation:

Answer 2

X=6

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