To identical spheres of radius 6 intersect so that the distance between their centers is 10. The points of intersection of the two spheres form a circle. What is the area of this circle?

Given the tetrahedron ABCD, O , E are the midpoints of BD and BC , respectively. CA=CB=CD=BD=2 , AB=AD=\sqrt{2} .

Given the right trapezoid ABCD , AB\parallel CD , AB\perp AD , AB=AD=\dfrac{1}{2}CD=1 . Now make a square ADEF with AD as one of its sides, and then fold the square along AD to make the plane ADEF is perpendicular to plane ABCD , M is the midpoint of ED .

Given the base of pyramid P-ABCD is a square. If the side of the square is 1 in length , PA\perp CD , PA=1 , PD=\sqrt{2} .

Prove PA\perp plabe ABCD

Given the triangular pyramid P−ABC , △PAB is an equilateral triangle, \angle PAC=\angle PBC=90° .

Prove AB\perp PC

Given the triangular pyramid P-ABC such that AC=BC=2 , \angle ACB = 90° , AP=BP=AB , PC\perp AC .

Given pyramid P-ABCD , its base ABCD is a right trapezoid, BA\perp AD , CD\perp AD , CD = 2AB , PA \perp base ABCD , E is the midpoint of PC , PA = AD .

Prove BE\perp plane PDC

Given the pyramid P- ABCD , AB⊥ plane PAD , AB\parallel CD , PD=AD , point E is the midpoint of PB , F is on CD , DF=\dfrac{1}{2}AB , PH is the height of △PAD originating from side AD .

(1) Prove PH⊥ plane ABCD

(2) If PH=1 , AD=\sqrt{2} , FC=1 , find volume of three sided pyramid E-BCF .

(3) EF⊥ plane PAB

Given the base of pyramid P-ABCD is a square, PA⊥ Base ABCD , ∠PDA=45° . E , F are the midpoints of edge AB and PD, respectively. Prove

(1) AF∥ Plane PCE

(2) Plane PCE⊥ Plane PCD

In the pyramid P-ABCD , △PBC is a right triangle, AB⊥ plane PBC , AB \parallel CD , AB = \dfrac{1}{2} DC . E is the midpoint of PD . Prove:

(1) AE \parallel plane PBC .

(2) AE ⊥ plane PDC