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  

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step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq