...figure. 4. One circle cannot touch another, either externally or internally, in more than one point. 5. The angle at the centre of a circle is double the angle at the circumference, standing on the same arc. 6. About a given circle to describe a triangle, equiangular to a given triangle....

...Theorem ; in consequence of which, it is said, lie offered a hecatomb to the gods. THEOREM VIII. An angle at the centre of a circle is double the angle at the circumference, when both stand on the same arc. Let ABC be a circle, and BDC an angle at the centre, and BAG an angle at...

...diameter. seg. The figure bounded by a chord of a circle and either arc cut off by it is called a segment. The angle at the centre of a circle is double the angle at the circumference standing on the same arc. The case of reflex angle is not necessary for the logical sequence nor for...

...then arc CD : arc EF < - . r .-. CAD : EBF= arc CD : arc EF. [Prop. 13. [Prop. 13. [Art. 46. (ii) An angle at the centre of a circle is double the angle at the circumference standing on the same arc. Hence the ratio of two angles at the centre of the same or of equal circles...

...any chord of the greater circle drawn from the point of contact is b.sected by the lesser circle. 6. The angle at the centre of a circle is double the angle at the circum- 1 3 f erence, when the angles stand on the same arc. Two circles whose centres are A and В...

...¿.ADB is said to stand on the arc ACB, whilst ¿.ACB stands on the arc ADB. 173. Proposition 10. An angle at the centre of a circle is double the angle at the circumference standing on the same arc. Let AEB (Fig. 141 (a)) be an arc of a circle of which 0 is the centre, and...