Modern geometry by Daniel Jamisola

danieljamisola0 — 2020-05-14 06:33:47 UTC

3.5.3 Fix a circle C1 with center O, a point A not on the circle, and point D on the circle, Now let B be the point of intersection of the line through O with the circle through Aand D that is orthogonal to C1.

danieljamisola0 — 2020-05-14 06:37:59 UTC

3.6.1 Let origin(1,2) and radius = 1

(x-h)²+(y-k)²=r²
(1-h)²+(2-k)²=1
1-2h+h²+4-4k+k²=1
4-2h+h²-4k+k²=0

danieljamisola0 — 2020-05-14 06:41:26 UTC

3.5.1 Circle C1 centered at O and a point D on this circle, construct a circle C2 intersecting C1 orthogonally at D.

danieljamisola0 — 2020-05-14 06:50:21 UTC

3.4.7 Definition. The area
Areah (P1P2KP) of a polygon P1P2KPn
is defined by
Areah (P1P2KPn) = k (P1P2KPn)

danieljamisola0 — 2020-05-14 06:50:41 UTC

3.5 Two circles intersect at right angles when the tangents to both circles at
their point of intersection are perpendicular.
Another way : the tangent to one of the circles at their point of intersection D passes through the center of the
other circle.

danieljamisola0 — 2020-05-14 06:55:17 UTC

3.4.5 Definition. The defect of triangle ABC is the number
( ABC) =180 −m A− m B−m C
More generally, the defect can be defined for polygons.

danieljamisola0 — 2020-05-14 06:58:20 UTC

3.6.3. Open a Poincaré Disk and construct a hyperbolic right triangle. (A right
triangle has one 90° angle.)

danieljamisola0 — 2020-05-14 07:17:53 UTC

3.6.5 (a) The opposite sides of a parallelogram are congruent. (A parallelogram is a quadrilateral
where opposite sides are parallel.)
(b) The measure of an exterior angle of a triangle is equal to the sum of the measure of the
remote interior angles.