In the given figure, ABCD is a quadrilateral inscribed in a circle with centre O. CD is produced to E such that ∠AED = 95° and ∠OBA = 30°. Find ∠OAC.

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Solution

We are given ABCD is a quadrilateral with center O, ∠ADE = 95° and ∠OBA = 30°

We need to find ∠OAC

We are given the following figure

Since ∠ADE = 95°

⇒ ∠ADC = 180 ° − 95° = 85°

Since squo;ABCD is cyclic quadrilateral

This means

∠ABC + ∠ADC = 180°

Since OB = OC (radius)

⇒ ∠OBC = ∠OCB = 65°

In ΔOBC

Since ÐBAC and ÐBOC are formed on the same base which is chord.

So

Consider ΔBOA which is isosceles triangle.

∠OAB = 30°

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Similar questions

In the figure, ABCD is a quadrilateral inscribed in a circle with centre O. CD produced to E such that $A E D = 95^{o}$ and $∠ O B A = 30^{o}$ . Find $∠ O A C$ .

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