Question

Prove this answer right with circle theorem.

Best answer I will give brainliest.​

Answer 1

i) OA = OB (Radii)

(ii) ∠OCA = ∠OAC

(angles opposite to equal sides are equal.)

(iii) In ΔAOC

∠<AOD = ∠OCA + ∠OAC

(Exterior angles of a triangle = Sum of the interior opposite angles)

(iv) ∠AOD = ∠OCA + ∠OCA

(substituting <OAC by <OCA)

(v) ∠AOD = 2∠OCA (by addition)

(vi) Similarly in triangle BOC

∠BOD = 2∠OCB

(vii) ∠AOD + ∠BOD = 2∠OCA + 2∠OCB

= 2(∠OCA + ∠OCB)

(∠AOD + ∠BOD = ∠AOB and ∠OCA + ∠OCB = ∠ACB)

(viii) ∠AOB = 2∠ACB

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