$\overline{\text{fh}}$ is tangent to circle g at point f.

what is the length of the radius, $r$?

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Question

$\overline{\text{fh}}$ is tangent to circle g at point f.

what is the length of the radius, $r$?

10 units
12 units
20 units
24 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Tangent Line to Circle", "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Tangent Line to Circle", "Pythagorean Theorem", "Circle Geometry" ] } ## Identify the right triangle and its side lengths $$ \begin{aligned} &\angle GFD = 90^\circ \quad (\text{since } \overline{FH} \text{ is tangent to circle } G \text{ at } F) \ &FH = 35 \ &FG = r \ &HG = 25 + r \end{aligned} $$ ## Apply the Pythagorean theorem to solve for r $$ \begin{aligned} &FG^2 + FH^2 = HG^2 \ &r^2 + 35^2 = (25 + r)^2 \ &r^2 + 1225 = 625 + 50r + r^2 \ &1225 = 625 + 50r \ &50r = 600 \ &r = 12 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the right triangle and its side lengths

Apply the Pythagorean theorem to solve for r

Answer: