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Type: Multiple-Choice
Category: Circles
Level: Grade 10
Author: nsharp1
Created: 7 years ago

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Circles Question

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Given the circle pictured below with diameter

$bar{AD}$ (not drawn), with

$bar{AB}$ tangent to the circle, and line

$bar{AC}$ also not drawn. Prove that

$triangle ABD \ ~ triangle CAD$ .

Circle with Secant CD and Tangent AB

$" Statement "$	$" Reason "$
$1. "Draw lines " bar(AD) \ & \ bar{AC}$	$1. "Two points create a line"$
$2. bar(AD) \ \ "is a diameter"$	$2. "Given"$
$3.$	$3. "Inscribed angle subtended by a diameter is a right angle"$
$4. bar(AB) \ \ "is tangent to the circle"$	$4. "Given"$
$5. bar{AB} _\|_ bar{AD}$	$5.$
$6. ang BAD \ \ "is a right angle"$	$6. "Definition of perpendicular lines"$
$7.$	$7. "All right angles are congruent"$
$8. ang ADC ~= ang ADB$	$8. "Reflexive property"$
$9. triangle ABD \ ~ triangle CAD$	$9.$

Grade 10 Circles

What is the missing reason in step 5?

Triangle ABD looks like a right triangle
Tangent lines intersect all lines at a right angle
A tangent line is perpendicular to the diameter
The Pythagorean Theorem