Urgent! ! ! A question about the circle, math in grade three.

This is the topic in the exercise book.

1): oc vertical AP in C, OD vertical PB in D. ..

∵PA=PB ∴OC=OD (in the same circle or in the same circle, the centers of equal chords are equidistant)

∴∠APO=∠BPO (points with equal distance to both sides of the angle are on the bisector of the angle)

(2): OE and OF are perpendicular to AC and BD respectively.

∵AC=BD ∴OE=OF (in the same circle or in the same circle, the centers of equal chords are equidistant)

In δδOPE and OPF.

1。 OP=OP (common edge) 2. OE=OF (known) 3. ∠PEO=∠PFO=90 degrees

∴ΔOPE Δ OPF (HL) ∴∠ APO = ∠ BPO ∴∴∴ PO ∠APB.

(3)

Connect AO, OB

From the figure, we can get OA, OB is the radius of the circle, ∴OA=OB.

PA = PB (known) OP=OP (male * * * side)

∴ΔopA ≌ΔOPB (SSS) ∴∠ OPA = ∠ OPE, that is, OP shares ∠APB.