Question was provided via image upload.

Question

Accepted Answer

{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Geometry", "Arc Measure", "Inscribed Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Circle Geometry", "Arc Measure", "Inscribed Angle Theorem" ] } ## Identify given geometric properties $$ \begin{aligned} &\text{BD is a diameter of circle } M \implies \text{arc } BCD = 180^\circ, \text{ arc } BAD = 180^\circ\ &\text{arc } CD = \text{arc } DA\ &\angle BCD = 90^\circ \quad (\text{inscribed angle subtending diameter } BD) \end{aligned} $$ ## Determine the measures of the arcs and central angles $$ \begin{aligned} &\text{From the diagram, } \angle BMC = 45^\circ \implies \text{arc } BC = 45^\circ\ &\text{arc } CD = 180^\circ - \text{arc } BC = 180^\circ - 45^\circ = 135^\circ\ &\text{Since } \text{arc } DA = \text{arc } CD \implies \text{arc } DA = 135^\circ\ &\text{Central angle } \angle AMD = \text{arc } DA = 135^\circ \end{aligned} $$ ## Calculate the measure of angle ADM $$ \begin{aligned} &MA = MD = r \implies \triangle AMD \text{ is isosceles with } \angle DAM = \angle ADM\ &\angle ADM = \frac{180^\circ - \angle AMD}{2} = \frac{180^\circ - 135^\circ}{2} = 22.5^\circ \end{aligned} $$

(A) $22.5^\circ$

(B) $30.0^\circ$

(C) $45.0^\circ$

(D) $67.5^\circ$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify given geometric properties

Determine the measures of the arcs and central angles

Calculate the measure of angle ADM

Answer: