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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In O (not shown), R S ¯ is a diameter and T is the midpoint of semicircle R T S ^ . What is the value of the ratio R T R S ? The ratio R T R O ?

To determine

To find:

To find value of the ratio RTRS and ratio RTRO.

Explanation

Given that, in O (not shown), RS¯ is a diameter and T is the midpoint of semicircle RTS^.

The diagrammatic representation is given below,

Given that RS¯ is diameter therefore, mRTS^=180°.

Then T is midpoint of RTS^. Therefore,

mRT^=mTS^=180°2=90°

That is mRT^=mTS^.

Therefore, RT=TS.

Also R and S on the circle to get the following,

mR=mTS^2=90°2=45°

mS=mRT^2=90°2=45°

Since inscribed angle are half of the arc length.

Since, RT=TS,OR=OS,andOT=OT.

By using SSS congruence to get the following,

ΔTORΔTOS

In congruent triangles corresponding parts are congruent (CPCTC). Therefore,

mTOR=mTOSmTOR=mTOS=90

A special type of right triangle is the 454590right triangle

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