Power of a point

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**Power**of a**point**. For external**points**, the**power**equals the square of the length of a tangent from the**point**to the circle. The**power**of a**point**is also known as the**point**‘s circle**power**or the**power**of a circle with respect to the**point**.

Contents

- 1 What is meant by power of a point?
- 2 How do you find the power of a point?
- 3 What is a point of a circle?
- 4 What is a power theorem?
- 5 How do you use power of a point?
- 6 What is mid point theorem Class 9?
- 7 What is the radical axis of two circles?
- 8 What is the value of angle in semicircle?
- 9 Does a point have radius?
- 10 How many points are in a circle?
- 11 Is a point also a circle?
- 12 What is a two chord power theorem?
- 13 What are the 3 power theorems?

## What is meant by power of a point?

In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle.

## How do you find the power of a point?

Indeed, if we take U and V as two intersection points of the line PO with the circle (O) then the power of the point P can be calculated as follows: When P is outside the circle PU times PV = (PO – r)(PO + r) = PO^2 – r^2. When P is inside the circle PU times PV = (r – PO)(r + PO) = r^2 – PO^2.

## What is a point of a circle?

The distance from a circle’s center to a point on the circle is called the radius of the circle. A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle. For the circle below, AD, DB, and DC are radii of a circle with center D.

## What is a power theorem?

If two chords of a circle intersect inside the circle, then the product of the measures of the segments of one chord is equal to the product of the measures of the other chord.

## How do you use power of a point?

Given a point P and a circle, pass two lines through P that intersect the circle in points A and D and, respectively, B and C. Then APcdot DP = BPcdot CP. The point P may lie either inside or outside the circle.

## What is mid point theorem Class 9?

The midpoint theorem states that “ The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

## What is the radical axis of two circles?

The radical axis of two circles is the locus of a point which moves such that the lengths of the tangents drawn from it to the two circles are equal.

## What is the value of angle in semicircle?

The angle at the circumference in a semicircle is 90°. Angles in a triangle add up to 180°.

## Does a point have radius?

Theoretically a point is a circle with no radius.

## How many points are in a circle?

So just as you need three points to define a triangle, you also need three points to define a circle, two points won’t do it.

## Is a point also a circle?

A real circle is exactly what you normally think of as a circle; it has a radius that is a real number (not imaginary). A point “circle” is just a point; it’s a circle with a radius of zero (hence a degenerate circle).

## What is a two chord power theorem?

Chord-Chord Power Theorem: If two chords of a circle intersect, then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord.

## What are the 3 power theorems?

There are three power theorems you can use to solve all sorts of geometry problems involving circles: the chord-chord power theorem, the tangent-secant power theorem, and the secant-secant power theorem. This unifying scheme can help you remember all three of the power theorems.