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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

Elementary Geometry For College St...

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

In Review Exercises 5 to 10, B A is tangent to the circle at point A in the figure shown.

G i v e n :           m B = 35 °   a n d   m D C ^ = 70 °

          F i n d :             m A D ^ ,   m A C ^

To determine

To find: mAD^, mAC^

Explanation

Theorem:

1) The measure of an angle formed when two secants intersect at a point outside the circle is one-half the difference of the measures of two intercepted arcs.

2) The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

Calculation:

Given that

mB=35°, mDC^=70° and BA is tangent to the circle at point A.

By theorem, the measure of an angle (mB) formed when two secants (BD and BA) intersect at a point (B) outside the circle is one-half the difference of the measures of two intercepted arcs AD^ and AC^ .

So, mB=12(mAD^-mAC^)

35°=12(mAD^-mAC)^

70°=mAD^-mAC^

mAD^-mAC^=70°

Now, mAD^+mAC^+mDC^=360°

mAD^+mAC^+70°=360°

mAD

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