Because DA is perpendicular to the x axis
So OAD angle =90 degrees.
So the triangle is a right triangle.
So db 2 = ad 2+ab 2
Because AB=OA-OB=5-2=3.
So DB=5
Because DB=PC
So PC=5
Because DC is perpendicular to the y axis
So the angle OCD=90 degrees.
Because angle OAD+ angle AOC+ angle OCD+ angle ADC=360 degrees
Angle AOC=90 degrees
So the angle ADC=90 degrees.
Therefore, angle ADC= angle OAD= angle AOC= angle OCD=90 degrees.
So the quadrilateral OADC is a rectangle
So AD=OC=4.
Angle COP=90 degrees
So the triangle OPC is a right triangle.
So PC 2 = oc 2+op 2.
So t=OP=3.
So when t=3 seconds, DB=PC.
(2) Solution: Because PC is perpendicular to BC.
So BCP angle = OCB angle +OCP angle =90 degrees.
Because angle AOC+ angle OBC+ angle OCB= 180 degrees.
Angle AOC=90 degrees
So OBC angle +OCB angle =90 degrees.
So Angel ·OBC = Angel ·OCP
Because the angle AOC=COP=90 degrees
So the triangle OBC is similar to the triangle COP (AA).
So OC/OB=OP/OC
Because OC=4 OB=2
So t=OP=8.
So when t=8 seconds, PC is perpendicular to BC.
(3) Solution: Because the circle P is tangent to one side of the triangle BCD, let the tangent point be E and connect PE.
So the angle PEC=90 degrees
Because the quadrilateral OADC is a rectangle (proved)
So AD=OC=4.
Angle θc = angle POC = 90 degrees.
Because angle OCE+ angle POC+ angle PEC+ angle OPE=360 degrees.
So the angle OPE=90 degrees.
So angle OCE= angle POC= angle PEC=OPE=90 degrees.
So the quadrilateral Organization of Petroleum Exporting Countries is a rectangle.
Because PO=PE
So the quadrilateral organization of petroleum exporting countries is a square.
So OP=OC=4.
So t=4
So when t=4 seconds, the circle with P as the center and OP as the radius is tangent to the straight line on one side of the triangle BCD.