Question

$\overleftrightarrow{hj}$ is tangent to $\odot g$. what is $hj$?

$hj = \square$ m

Explanation:

Step1: Apply the Pythagorean theorem

Since \( \overleftrightarrow{HJ} \) is tangent to \( \odot G \), \( \angle GHJ = 90^{\circ} \) (tangent - radius property). In right - triangle \( GHJ \), by the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( c = GJ=29\) m (hypotenuse) and \( a = GH = 21\) m (one leg), and \( b=HJ\) (the other leg). So \( HJ=\sqrt{GJ^{2}-GH^{2}} \).

Step2: Substitute the values

Substitute \( GJ = 29\) and \( GH = 21\) into the formula: \( HJ=\sqrt{29^{2}-21^{2}}=\sqrt{(29 + 21)(29 - 21)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)). Then \( HJ=\sqrt{50\times8}=\sqrt{400}\).

Step3: Calculate the square root

\(\sqrt{400}=20\).

Answer:

\(20\)