Proposition III.34 — From a given circle to cut off a segment admitting an angle …

Proof

Let the circle and angle

θ

be given. Draw a tangent

B C

to the circle by III.17. At the point of contact

B

, construct

∠ C B D = θ

in the half-plane that intersects the circle (I.23). Let

B D

meet the circle at

D

. The chord

B D

cuts off two segments; the segment on the far side of

B D

from the tangent admits the inscribed angle

θ

by III.32 (tangent-chord angle).

Knowledge graph · drag to pan, scroll to zoom, click a node to navigate

Full neighborhood

Depends on (3)

III.17Proposition III.17From a given point to draw a straight line touching a given circle.
III.32Proposition III.32If a straight line touch a circle, and from the point of contact there be drawn across, in the circle, a straight line…
I.23Proposition I.23On a given straight line and at a point on it to construct a rectilineal angle equal to a given rectilineal angle.

Discussion

No replications, contradictions, or comments registered yet for this claim.

Replicate or annotate this claim

Replicate to register a fresh attempt; contradict, extend, or comment otherwise. Authors can post a claim-retraction with the reason taxonomy from RRP-0020.