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^@#