ACT Preparation / Unit 14 ACT 1310 worked example, 60 to 90 seconds
Using an Inscribed Angle
The idea
Inscribed-angle problems are solved in three steps. First, find the arc the angle intercepts: the arc between the angle's two sides, on the side away from its vertex. Second, if a central angle stands on the same arc, the arc's measure equals the central angle. Third, halve the arc for the inscribed angle, or double an inscribed angle to recover the arc.
In practice
Worked example: in a circle with center O, central angle AOB is 120°, and point C lies on the circle on the far side from arc AB. Arc AB measures 120°, so inscribed angle ACB is 60°. Second: triangle PQR is drawn in a circle with PR a diameter. Angle Q intercepts a semicircle, so angle Q is 90°, and if angle P is 35°, angle R is 55°.
Where people slip
Two inscribed angles that intercept the same arc are equal, wherever their vertices sit on the rest of the circle.
Your place on the trail
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Builds on
Unlocks
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