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In the circle below AD is a diameter and AB is tangent at A suppose mADC=224° find the measure of m

In the circle below AD is a diameter and AB is tangent at A suppose mADC=224° find-example-1
User Rbanffy
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1 Answer

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The measure of angle CAB is 68⁰.

The measure of angle CAD is 22⁰.

How to calculate the measure of the missing angles?

The measure of the missing angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

The measure of arc ACB is calculated as;

arc ACB = 360 - arc ADC (sum of angles in a circle)

arc ACB = 360 - 224

arc ACB = 136

The measure of angle CAB is calculated as;

m∠CAB = ¹/₂ (arc ACB) (intersecting chord theorem)

m∠CAB = ¹/₂ x 136

m∠CAB = 68⁰

The measure of angle CAD is calculated as;

m∠CAD = 90 - m∠CAB (complementary angles add up to 90 degrees)

m∠CAD = 90 - 68

m∠CAD = 22⁰

User Rioualen
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