As shown in the figure, a, B, C and D are the four points on the circle O, and the verification of AC / / BD, OA ⊥ ob is ad ⊥ BC

As shown in the figure, a, B, C and D are the four points on the circle O, and the verification of AC / / BD, OA ⊥ ob is ad ⊥ BC


∵OA==OB,OA⊥OB
The AOB is an isosceles right triangle
∴∠OAB=∠OBA=45°
∵AC∥BD
∴∠DBA+∠CAB=180°
∠BDC+∠ACD=180°
∴∠DBO+∠CAO=90°
∵OB=OD,OC=OA
∴∠BDO=∠DBO,∠CAO=∠ACO
∴∠BDO+∠ACO=90°
∴∠ODC+∠OCD=90°
∴∠COD=90°
∵∠AOB=∠COD=90°
OA=OB=OC=OD
∴△AOB≌△COD
∴AB=CD
∴AB∥CD
The abdc is a parallelogram
∴AC=BD
∵OA=OB=OC=OD
∴△AOC≌△BOD(SSS)
∴∠BOD=∠AOC
∵∠BOD+∠AOC=360°-∠AOB-∠COD=360°-90°-90°=180°
∴∠BOD=∠AOC=90°
∴∠AOB+∠BOD=180°
∠BOD+∠COD=180°
A, O and D are on the same line
B. O and C are on the same line
∴AD⊥BC



It is known that OA and ob are the two radii of circle O, CD are on OA and ob respectively, and AC = BD. what is the size relationship between AD and BC? Please


I can't draw a picture. It's not easy to show. Let me give you an example
If AB is connected, then OAB is an isosceles triangle;
Connect CD, because AC = BD, you can get OC = OD, triangle OCD is also isosceles triangle;
If CD and ab are parallel, the quadrilateral abdc is an isosceles trapezoid
So ad = BC