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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Given circle P and points R P T such that R and T are in the exterior of circle P , suppose that tangents are constructed from R and T to form a quadrilateral (as shown). Identify the type of quadrilateral formed

a) when R P > P T .

b) when R P = P T .

Chapter 6.4, Problem 14E, Given circle P and points RPT such that R and T are in the exterior of circle P, suppose that

To determine

(a)

To identify:

The type of quadrilateral formed based on the condition when RP>PT.

Explanation

A quadrilateral in which two pairs of adjacent sides are equal and diagonals intersect at 90° and only one diagonal is bisected by the other is called a kite. Thus, in a kite AB=AD and BC=CD. Also, AEB=AED=BEC=DEC=90°.

The line that is perpendicular to the radius of a circle at its endpoint on the circle is a tangent to the circle. The tangents from an exterior point to the circle are two in numbers and the length of both is same at the point of intersection of the circle. In the figure below from point S two tangents are drawn touching the circle at R and T,

So, SR=ST

To determine

(b)

To identify:

The type of quadrilateral formed based on the condition when, RP=PT.

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