In circle ( G, G H=6 ) and ( mathrm{m} angle H G I=90^{circ} ). Find the length of ( H I ). Express your answer as a fraction times ( pi ).

Question

Accepted Answer

Step:1 ：1. Use the theorem that the angle subtended by a diameter in a circle is always a right angle: Since (mathrm{m}angle HGI = 90^{circ}), we know that GI is a diameter.Step:2 ：2. Use the Pythagorean theorem on right triangle HGI: (GH^2+HI^2 = GI^2)Step:3 ：3. Calculate HI: (HI^2 = GI^2 - GH^2) and (HI = sqrt{GI^2 - GH^2})

Answer

Step: 1 ：1. Use the theorem that the angle subtended by a diameter in a circle is always a right angle: Since (mathrm{m}angle HGI = 90^{circ}), we know that GI is a diameter.Step: 2 ：2. Use the Pythagorean theorem on right triangle HGI: (GH^2+HI^2 = GI^2)Step: 3 ：3. Calculate HI: (HI^2 = GI^2 - GH^2) and (HI = sqrt{GI^2 - GH^2})

In circle $G, G H = 6$ and $m ∠ H G I = 90^{\circ}$ . Find the length of $H I$ . Express your answer as a fraction times $π$ .

Answer

Popular Problems

In circle G,GH=6 and m∠HGI=90∘. Find the length of HI. Express your answer as a fraction times π.

Answer

Popular Problems

In circle $G, G H = 6$ and $m ∠ H G I = 90^{\circ}$ . Find the length of $H I$ . Express your answer as a fraction times $π$ .