Question

leo is constructing a tangent line from point q to circle p. what is his next step?options:construct a circle from point q with the radius pr;construct the perpendicular bisector of segment pq;construct a circle from point r with the radius rp;construct the perpendicular bisector of segment rq.question 8a circle is represented by the equation below:$(x - 5)^2 + (y + 7)^2 = 49$which statement is true?options:the circle is centered at $(-5, 7)$ and has a radius of 7;the circle is centered at $(5, -7)$ and has a diameter of 7;the circle is centered at $(5, -7)$ and has a radius of 7;the circle is centered at $(-5, 7)$ and has a diameter of 7

Explanation:

First Question:

Step1: Recall tangent construction steps

To construct a tangent from an external point \(Q\) to circle \(P\), the first step is to find the midpoint of segment \(PQ\) (done by constructing its perpendicular bisector, which is what the existing arcs indicate is in progress, identifying \(R\) as the midpoint). The next step is to draw a circle with midpoint \(R\) as the center, using \(RP\) (or \(RQ\), since \(R\) is the midpoint) as the radius. This circle will intersect the original circle at the tangent points.

Step2: Match to options

The correct next step aligns with constructing a circle from \(R\) with radius \(RP\).

The standard form of a circle's equation is \((x-h)^2 + (y-k)^2 = r^2\), where \((h,k)\) is the center and \(r\) is the radius. For the given equation \((x - 5)^2 + (y + 7)^2 = 49\), rewrite \(y+7\) as \(y-(-7)\), so \(h=5\), \(k=-7\), and \(r^2=49\), meaning \(r=7\).

Answer:

Construct a circle from point R with the radius RP

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Second Question: