How do you find ABC?

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Answer 1 · 2018-05-15T18:35:18

$color(blue)(210^@$

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The bisector of $/_ CDA$ always passes through the centre.

Also, the radius is perpendicular to the tangent line at the point of tangency.

$/_CDB=/_ADB=15^@$

$/_CED=/_AED=180-(15+90)=75^@$

Measure of $AFC=2*75=150^@$

Measure of $ABC=360-150=210^@$

There is also a formula for this:

Let $AFC=x$

Then $ABC=360-x$

$((360-x)-x)/2=/_CDA=30^@$

$360-2x=60$

$x=150=AFC$

$ABC=360-AFC=210^@$