The centers of two circles are E and G, and they have radii 5 cm and 12 cm respectively. The distance between E and G is 13 cm. Show that the angle at F is 90 degrees.

April 18, 2026Mathematics

ScanSolve AI Answer

April 18, 2026

Answer

90^\circ$.

Step 1: Show that $\angle EFG = 90^\circ$ . Given the radii of the circles and the distance between their centers: • Radius of circle E, $EF = 5 \text{ cm}$ . • Radius of circle G, $GF = 12 \text{ cm}$ . • Distance between centers, $EG = 13 \text{ cm}$ .

Consider the triangle $\triangle EFG$ . We check if the Pythagorean theorem holds for its sides: $EF^2 + GF^2 = 5^2 + 12^2 = 25 + 144 = 169$ $EG^2 = 13^2 = 169$ Since $EF^2 +

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Show that EFG = 90^. Given the radii of the circles and the distance between their centers: • Radius of circle E, EF = 5 cm.

Asked on April 18, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 18, 2026

Step 1: Show that EFG = 90^. Given the radii of the circles and the distance between their centers: • Radius of circle E, EF = 5 cm. • Radius of circle G, GF = 12 cm. • Distance between centers, EG = 13 cm. Consider the triangle EFG. We check if the Pythagorean theorem holds for its sides: EF^2 + GF^2 = 5^2 + 12^2 = 25 + 144 = 169 EG^2 = 13^2 = 169 Since $EF^2 +