PROBLEM XVII.

To draw a Tangent to a given circle, that shall pass through a given point A, in the circle.

D

A

Draw the radius A O.

Erect a perpendicular at the end of it A.
Produce the perpendicular to D.
CD, will be the Tangent required.

C

CASE II.-When the given point A, is without

the circle.

B

D

A

Draw a line A B from the given point, to the centre of the circle B.

Bifect A B, in C.

With the radius C B or C A, and C for a centre, defcribe the femicircle A DB, cutting the given circle in D.

Draw A D, which will be the Tangent required.

PROBLEM XVIII.

To infcribe a Circle, in a given triangle ABC.

C

D

Bifect any two angles with two lines, these lines will interfect in the point D, which is the centre of the Circle.

Set one point of the compaffes in D, and open them till the other point will touch any fide of the triangle without paffing through it, with that radius defcribe the Circle.

PROBLEM XIX.

To inscribe an Equilateral Triangle, in a Circle.

With the radius of the circle, and any point A in the circumference as a centre, describe the arc B C.

Draw the line B C, which will be the fide of the Equilateral Triangle required.

D

PROBLEM XX.

To inscribe a Square, in a given circle ABCD.

Draw two diameters A B and C D, croffing each other

at right angles.

Draw the lines AD, DB, BC and A C, which will form the Square required.

PROBLEM XXI.

To infcribe a Pentagon, in a given circle.

Draw two diameters A B and C D, at right angles. Bifect a radius E D, in F.

With the radius F A, and F as a centre, defcribe the arc AG.

The distance AG, is the fide of the Pentagon required.

PROBLEM XXII.

To infèribe an Hexagon, in a given circle.

O

Take the radius of the circle, and carry fix times round the circumference.