As shown in the figure, AB and CD intersect at the point O, O is the midpoint of AB, ∠ a = ∠ B, is Δ AOC and Δ BOD congruent? Why?

As shown in the figure, AB and CD intersect at the point O, O is the midpoint of AB, ∠ a = ∠ B, is Δ AOC and Δ BOD congruent? Why?

Congruent, ∠ a = ∠ B, OA = ob, ∠ AOC = ∠ BOD (equal to vertex angle), ASA, so congruent

As shown in the figure, the straight lines AB and CD intersect at the point O. if ∠ AOC + ∠ BOD = 70 ° is known, then ∠ BOC=______ .

∵∠AOC+∠BOD=70°，
And ∵ AOC = ∵ BOD,
∴∠AOC=∠BOD=35°．
∴∠BOC=180°-∠AOC=180°-35°=145°．
So the answer is: 145 degrees

It is known that arc AB and CD are two arcs of circle O, and arc AB = 2 arc CD, then the relationship between chord AB and 2CD is AB>2CD AB

AB<2CD

In the circle O, AB and CD are the chords of circle O, ab = 2CD

If the midpoint of AB is m, then am = BM = CD, with a and B as the center of the circle, and am and BM as the radius, then there must be an intersection point E and F on the arc an and arc BN because the chord AE = BF = AB / 2 = CD, so arc AE = arc BF = arc CD because of the arc AB = arc a

In the same circle, if AB=2 CD, then the relationship between string AB and CD is ab______ 2CD．

As shown in the figure,
AB=2
CD，
CD=
BE=
AE，
A kind of
CD=
BE=
AE，
∴AE=BE=CD，
In △ Abe, AE + be > ab,
∴AB＜2CD．
So the answer is: <

If there are two strings AB and Cd in circle O, and ab = 2CD, can the relationship between arc AB and arc CD be determined

No, you don't even know what's going on

In 0o, the chord center distance of chord AB is equal to half of the chord length, and the arc length of the chord is 47 π cm. Try to find the radius of 0o

In 0o, the chord center distance h of chord AB is equal to half of the chord length L, and the arc length of the chord is C = 47 π cm. Try to find the radius r? Of 0 o?
The center angle of the arc is a
A=2*ARC TAN((L/2)/(L/2)
=2*ARC TAN(1)
=90 degrees
=90*PI/180
=1.5708 radians
R=C/A=47*π/1.5708=94cm

(1) if om = on, prove that arc AC = arc BD (2) If arc AC = arc BD, prove: EO bisection angle AED As shown in the figure, it is known that in the circle O, the two chords AB and CD of circle O are crossed by a point E in the circle O, AE = de. it is proved that arc AC = arc BD

The secant theorem AE * be = CE * De, because AE = De, CE = be, and ∠ AEC = ∠ DEB

As shown in the figure, in circle O, CD is the diameter, AB is the chord, D is the midpoint of arc AB, CD = 10, DM: cm = 1:4, find the length of chord ab

If M is the intersection point of CD and AB, then there is:
CMA is equal to CD of CMB, vertical ab
Again, CBM is approximate to BDM and approximate to CDB
（10*（4/（4+1）））/（1/2AB）= （1/2AB）/（10*（1/（1+4））） AB=8

AB is the diameter of circle O, BC is the chord, OD ⊥ CB is at point E, intersection bcfu is at point D, if BC = 8, ed = 2, find the length of AC I just lost a fu

AC=6
Connect AC, OC;
Since AB is the diameter of the circle, the triangle ABC is a right triangle with ∠ C as the angle of RT,
At the same time, in RT △ OCD, let the radius be r, according to Pythagorean theorem
R ^ 2 - (8 / 2) ^ 2 = (R-2) ^ 2; the solution, r = 5, in RT △ ABC, from Pythagorean theorem, AC = 6