Question

hj is tangent to ⊙g. what is gj? 12 yd g gj = yd

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle{HGJ}=90^{\circ}$, and triangle $HGJ$ is a right - triangle.

Step2: Apply Pythagorean theorem

In right - triangle $HGJ$, if $HG = 12$ yd and $HJ=5$ yd, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $GJ$ is the hypotenuse, so $GJ=\sqrt{HG^{2}+HJ^{2}}$.

Step3: Calculate the value of $GJ$

Substitute $HG = 12$ and $HJ = 5$ into the formula: $GJ=\sqrt{12^{2}+5^{2}}=\sqrt{144 + 25}=\sqrt{169}=13$ yd.

Answer:

13