Angle BAC Solution: Circle Geometry

Name: Angle BAC Solution: Circle Geometry
Uploaded: 2026-07-18T14:03:26.125Z
Duration: 142 s
Description: Step-by-step solution for the semicircle diagram: from ∠OAB = 20° and OC ⊥ AB, show △OAB is isosceles, find central ∠AOB = 140°, bisect to ∠BOC = 70°, then…

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Angle BAC Solution: Circle Geometry

0:00 / 2:22

Finding Angle BAC

0:00 - 0:18

Problem setup: semicircle center O, OC perpendicular to chord AB, and ∠OAB = 20°.

△OAB is isosceles

0:18 - 0:42

OA and OB are radii, so base angles are equal: ∠OBA = 20°.

Central angle AOB

0:42 - 1:03

Angle sum in △OAB gives ∠AOB = 180° − 20° − 20° = 140°.

OC bisects ∠AOB

1:03 - 1:28

Perpendicular from the center bisects the apex angle: ∠AOC = ∠BOC = 70°.

Inscribed angle theorem

1:28 - 1:46

∠BAC intercepts arc BC; the matching central angle is ∠BOC = 70°.

∠BAC = 35°

1:46 - 1:57

Inscribed angle is half the central angle: ½ × 70° = 35°.

Recap

1:57 - 2:17

Radii → 140° central angle → 70° bisected angle → inscribed angle 35°.

Outro

2:17 - 2:22

Final answer: measure of angle BAC is 35°.