As shown in the figure, AB is the chord of OD, and the radius OC and OD intersect AB at points E and f respectively, and AE = BF. Verify that OE = of

As shown in the figure, AB is the chord of OD, and the radius OC and OD intersect AB at points E and f respectively, and AE = BF. Verify that OE = of

∵ AB is a chord of circle O, OD ⊥ ab ᚉ AC = BC = 1 / 2Ab, arc ad = arc BD (vertical diameter theorem)

As shown in the figure, AB is the chord of ⊙ o, the radius OC ⊥ AB is at point D, and ab = 6cm, OD = 4cm, then the length of DC is______ cm．

Connect OA,
∵OC⊥AB，AB=6cm，
∴AD=1
2AB=1
2×6=3cm，
In RT △ AOD,
∵OA=
OD2+AD2=
42+32=5cm，
∴DC=OC-OD=5-4=1cm．
So the answer is: 1

AB is the chord of circle O, the radius OC is parallel to ab. and ab = 6cm, OD = 4cm, find the length of DC

(1) Proof: CD is the tangent of semicircle. (2) if the length of AB is 4, the point d moves on the semicircle. If OC of ad is parallel to the chord ad, the angle ADO = angle doc, angle cob = angle Dao, because od = OA = ob, so the angle

As shown in the figure, AB is the chord of ⊙ o, the radius OC and OD intersect AB at points E and f respectively, and AE = BF. Please use three different methods to prove: OE = of

Method 1:
Connect OA and ob, as shown in the figure,
∵OA=OB，
∴∠OAE=∠OBF，
AE = BF,
∴△AOE≌△BOF（SAS），
∴OE=OF；
Method 2:
Make om ⊥ AB in M,
∵OM⊥AB，
∴AM=BM，∠EMO=∠FMO=90°，
∵AE=BF，
∴EM=FM，
Om = OM,
∴△OEM≌△OFM，
∴OE=OF；
Law 3:
The extension of CO, do and circle intersection with G, H,
From the intersecting string theorem,
AE•BE=CE•EG，
BF•AF=DF•HF，
∵AE=BF，
∴AF=BE，
∴CE=DF，
∴OE=OF．

As shown in the figure, OC and OA on both sides of the square aocb are located on the x-axis and y-axis respectively. The coordinates of point B are B (- 2 times the root sign 2, 2 times the root sign 2), and D is a point on the AB side The triangle ADO is folded along the straight line od so that point a just falls on the point E on the diagonal ob. if the point E is on an image of the inverse scale function Y1 = K1 / x, (1) calculate the function value Y1 when the inverse scale function is x = - 3. (2) set the analytic formula of the diagonal line ob as y2 = k2x, and get the value of K2. (3) complete the image of Y1 = K1 / x, and write the value range of X when Y1 is greater than Y2 according to the image,

To solve all this, we must first find the coordinates of the e point
Because OE is equal to 0A and OA is equal to two times the root 2, the coordinates of E are (- 2,2)
Substituting it into Y1 = K1 / x, we get K1 = - 4
Because B (- 2 times the root sign 2,2 times the root sign 2), replace it into y2 = k2x to obtain K2 = - 1
The third step is to draw the graph Y1 = K1 / X and y2 = k2x. When Y1 is greater than Y2, X is greater than - 2 and less than 0 and X is greater than 2

As shown in the figure, in the plane rectangular coordinate system, the two sides of the rectangular oabc are on the x-axis and y-axis respectively, OA = 8 times the root sign 2, OC = 8, and the existing two moving points P and Q are respectively from O P moves uniformly along the direction of OA at the speed of 1cm per second on the line OA. The movement time is T seconds (1) The area s of ▷ OPQ is expressed by the formula containing t (2) Verification: the area of quadrilateral opbq is a fixed value, and the fixed value is obtained;

(1) S triangle OPQ = 1 / 2 * OP * OQ
=1/2*√2t*(8-t)
=4√2t-(√2/2)t²
(2) S quadrilateral opbq = s trapezoid oqba-s triangle BPA = 1 / 2 * (OQ + AB) * oa-1 / 2op * ab
=8 radical 2 * 1 / 2 * (8-radical 2 * t) + 2T * 8 * 1 / 2
=32 root sign 2

In ⊙ o, if the chord AB is 2 2 cm, chord center distance is 2 cm 2 cm, then the circular angle of the chord is equal to______ .

As shown in the figure, if OA and ob are connected, ab = 2
2cm，OC=
2cm，
∵OC⊥AB，
∴AC=1
2AB=
2（cm），
∴OC=AC，
∴∠AOC=45°，
∴∠AOB=90°，
∴∠ADB=1
2∠AOB=45°，
∴∠AEB=180°-∠ADB=135°．
The circular angle of the chord is equal to 45 ° or 135 °
So the answer is: 45 ° or 135 °

It is known that in circle O, the length of chord AB is three times the root of radius OA, and point C is the midpoint of arc ab. what figure is the quadrilateral oacb and why? Sorry, wrong number. Root three

What does the root three times mean? If it is three times of the root OA, it is a rhombus... Connecting OC, crossing AB at point D, OC perpendicular to AB, obtained from the Pythagorean theorem, OC, AB is vertically bisected, and fixed into diamond

Known: as shown in the figure, in ⊙ o, the length of chord AB is radius OA AB and OC intersect at point P. it is proved that the quadrilateral oacb is rhombic

Prove that: ∵ C is
The midpoint of AB, OC is the radius,
∴PA=PB，AB⊥OC，
∵AP=1
2AB=
Three
2AO，
∴OP=
AO2−AP2=
AO2−3
4AO2=1
2OA=1
2OC，
∴PC=1
2oC, i.e., Op = PC,
The quadrilateral oacb is a parallelogram,
And ∵ ab ⊥ OC,
The quadrilateral oacb is rhombic

Known: as shown in the figure, in ⊙ o, the length of chord AB is radius OA AB and OC intersect at point P. it is proved that the quadrilateral oacb is rhombic

Prove that: ∵ C is
The midpoint of AB, OC is the radius,
∴PA=PB，AB⊥OC，
∵AP=1
2AB=
Three
2AO，
∴OP=
AO2−AP2=
AO2−3
4AO2=1
2OA=1
2OC，
∴PC=1
2oC, i.e., Op = PC,
The quadrilateral oacb is a parallelogram,
And ∵ ab ⊥ OC,
The quadrilateral oacb is rhombic