Q3 of 55 Page 1

In Figure 2, AB and AC are tangents to the circle with center O such that ∠BAC = 40°. Then calculate ∠BOC.

Given: AB and AC are tangents to the circle and ∠ BAC = 40°.


Since, AB and AC are tangents to the circle,



Therefore, ∠ OBA = ∠ ACO = 90°.


Since, ABOC is a quadrilateral, therefore sum of all angles of a quadrilateral is 360°.


∴ ∠ BAC + ∠ ACO + ∠ BOC + ∠ OBA = 360°


⇒ ∠ BOC = 360° - ∠ BAC - ∠ ACO - ∠ OBA


= 360° - 40° - 90° - 90°


= 140°


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