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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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Quadrilateral A B C D is inscribed in circle P (not shown). If A is an acute angle, what type of angle is C ?

To determine

To find:

The type of angle is C.

Explanation

Given:

Quadrilateral ABCD which is inscribed in circle P and A is an acute angle.

Property Used:

The measure of an inscribed angle of a circle is half the measure of its intercepted arc. Consider the figure below, let the inscribed angle be 2.

Then m2=12mHJ and generally HKKJ.

Calculation:

Suppose ABCD is a quadrilateral inscribed in circle P and A is an acute angle

Since, the measure of an inscribed angle of a circle is half the measure of its intercepted arc therefore mA=12mBCD and mC=12mDAB.

But, mBCD+mDAB=360°

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