Answer:
BD = CA ⇒ Proved down
Step-by-step explanation:
From the given figure
∵ AB and CD are diameters in circle O
∴ OB = OA = OC = OD ⇒ radii
∵ AB ∩ CD at O
∴ ∠BOD and ∠COA are vertically opposite angles
∵ The vertically opposite angles are equal in measures
∴ m∠BOD = m∠COA
→ In Δ OBD and Δ OCA
∵ m∠BOD = m∠COA ⇒ vertically opposite angles
∵ OB = OC ⇒ radii
∵ OD = OA ⇒ radii
∴ Δ OBD and Δ OCA are congruent by SAS postulate
→ From congruency
∴ BD = CA
