Question 1158197: A circle goes through the points A, B, C, and D consecutively. The chords AC and BD intersect at P. Given that AP = 6, BP = 8, and CP = 3, how long is DP?
Answer by ikleyn(52818)   (Show Source):
You can put this solution on YOUR website! .
For these chords and their parts, there is this metric relation
|AP| * |CP| = |BP| * |DP|,
or
6 * 3 = 8 * |DP|,
which gives you |DP| =  =  =  . ANSWER
Solved.
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See the lesson
- The parts of chords that intersect inside a circle,
in this site.
For theory lessons in this site on circles, their chords, secant and tangent lines see
- A circle, its chords, tangent and secant lines - the major definitions,
- The longer is the chord the larger its central angle is,
- The chords of a circle and the radii perpendicular to the chords,
- A tangent line to a circle is perpendicular to the radius drawn to the tangent point,
- An inscribed angle in a circle,
- Two parallel secants to a circle cut off congruent arcs,
- The angle between two chords intersecting inside a circle,
- The angle between two secants intersecting outside a circle,
- The angle between a chord and a tangent line to a circle,
- Tangent segments to a circle from a point outside the circle,
- The converse theorem on inscribed angles,
- The parts of chords that intersect inside a circle,
- Metric relations for secants intersecting outside a circle and
- Metric relations for a tangent and a secant lines released from a point outside a circle
- Quadrilateral inscribed in a circle
- Quadrilateral circumscribed about a circle
For lessons on solved problems for circles, their chords, secant and tangent lines see
- HOW TO bisect an arc in a circle using a compass and a ruler,
- HOW TO find the center of a circle given by two chords,
- Solved problems on a radius and a tangent line to a circle,
- Solved problems on inscribed angles,
- A property of the angles of a quadrilateral inscribed in a circle,
- An isosceles trapezoid can be inscribed in a circle,
- HOW TO construct a tangent line to a circle at a given point on the circle,
- HOW TO construct a tangent line to a circle through a given point outside the circle,
- HOW TO construct a common exterior tangent line to two circles,
- HOW TO construct a common interior tangent line to two circles,
- Solved problems on chords that intersect within a circle,
- Solved problems on secants that intersect outside a circle,
- Solved problems on a tangent and a secant lines released from a point outside a circle and
- The radius of a circle inscribed into a right angled triangle
- Solved problems on tangent lines released from a point outside a circle
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lessons are the part of this online textbook under the topic "Properties of circles, inscribed angles, chords, secants and tangents ".
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
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