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SECTION IV.

OF THE PROPERTIES OF THE CIRCLE.

*

QUERY I.

In how many points can a straight line CD, cut the circumference of a circle?

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A. In two points M, N, only. For, dropping from the centre of the circle the perpendicular OP upon the straight line CD, there is but one point in the line CD, on each side of the perpendicular, such, that a line, drawn from it to the point O of the perpendicular, has the length of the radius ON. (page 63, 6thly.)

* Before entering on this section, the teacher ought to recapitubate with his pupils the definitions of a circle, of an arc, of a chord, a segment &c. (page 9.)

SECTION IV.

OF THE PROPERTIES OF THE CIRCLE.*

QUERY I.

In how many points can a straight line CD, cut the circumference of a circle?

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A. In two points M, N, only. For, dropping from the centre of the circle the perpendicular OP upon the straight line CD, there is but one point in the line CD, on each side of the perpendicular, such, that a line, drawn from it to the point o of the perpendicular, has the length of the radius ON. (page 63, 6thly.)

* Before entering on this section, the teacher ought to recapitubate with his pupils the definitions of a circle, of an arc, of a chord, a segment &c. (page 9.)

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their centres, O and P, is less than the sum of their radii OM, PM.

QUERY III.

When do two circles

touch each other interiorly?

A. When the dis

tance OP, between

their centres, O and P,

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is equal to the sum of their radii OM, PM.

QUERY IV.

When do two circles touch each other interiorly?

A. When the distance OP between their centres, O and P, is equal to the difference between their radii, OM and PM.

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