How to do f and question 4 find angle COD for question 4 4 In the figure, AB is a tangent to the circle with centre O, D is the mid point of the chord BC Given the acirc; circ; nbsp;BAC=xo, find acirc; circ; nbsp; COD in terms of x

Varun Rawat answered this

In ∆ ODC and ∆ ODB ∠ ODC = ∠ ODB (90 ° each) OC = OB (radii of same circle) OD = OD [common] \Rightarrow ∆ ODC ≅ ∆ ODB (RHS) \Rightarrow ∠ COD = ∠ BOD (CPCT) \Rightarrow ∠ BOC = 2 ∠ COD Now, ∠ BOA + ∠ BOC = 180 ° (Linear pair) \Rightarrow ∠ BOA + 2 ∠ COD = 180 ° \Rightarrow ∠ BOA = 180 ° - 2 ∠ COD In ∆ OBA ∠ OAB + ∠ BOA + ∠ OBA = 180 ° (Angle sum property) \Rightarrow x + 180 ° - 2 ∠ COD + 90 ° = 180 ° \Rightarrow x + 90 ° = 2 ∠ COD \Rightarrow ∠ COD = \frac{x}{2} + 45 °