Question

hj is tangent to ⊙g. what is gj? 4 yd 3 yd gj = yd submit work not feeling ready yet pythagorean theorem (100) lesson: tangent to a circle

Explanation:

Step1: Recall tangent - radius property

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

Step2: Apply Pythagorean theorem

In right - triangle $\triangle GHJ$, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 3$ (length of $GH$), $b = 4$ (length of $HJ$), and $c$ is the length of $GJ$. So, $GJ=\sqrt{3^{2}+4^{2}}$.

Step3: Calculate the value of $GJ$

$GJ=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

$5$