Question

ABC triangle 0 The center of the circle and  ∠BAC = 50 if ∠obc = ?​

Answer 1

Answer:

Angle BAC =50

Since O is the circumcenter and angle BOC is the angle subtended by the arc BC at the center and angle BAC is the angle subtended by arc BC at. any point in the alternate segment hence

angleBOC= twice the angle BAC=100⁰

In triangle OBC

OB=OC both being radii of the circle

Hence angleOBC=angle OCB

angleOBC+angle OCB+angle BAC=180⁰

angleOBC+angle OCB=180⁰-angle BAC

angleOBC+angle OCB=180⁰-100⁰=80⁰

Hence angleOBC=80⁰/2=40⁰

Answer 2

Answer:

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Since O is the circumcenter, OA = OB + OC (being the radii of the circle). Hence triangles AOC, AOB AND BOA are and angles OAC = OCA; OBA = OAB and OBC = OCB.

Step-by-step explanation:

Angle BAC =50

Since O is the circumcenter and angle BOC is the angle subtended by the arc BC at the center and angle BAC is the angle subtended by arc BC at. any point in the alternate segment hence

angleBOC= twice the angle BAC=100⁰

In triangle OBC

OB=OC both being radii of the circle

Hence angleOBC=angle OCB

angleOBC+angle OCB+angle BAC=180⁰

angleOBC+angle OCB=180⁰-angle BAC

angleOBC+angle OCB=180⁰-100⁰=80⁰

Hence angleOBC=80⁰/2=40⁰