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Question
In the given circle with center o, ∠ABC=100°, ∠ACD=40° and CT is tangent to the circle at C. find ∠ADC and ∠DCT.
Solution
In a cyclic quadrilateral ABCD,
`∠ ABC+∠ADC=180°` (Opposite angle of a cydic quadrilateral are supplementary)
`⇒ 100°+∠ADC=180°`
`⇒ ∠ADC=80°`
Now, in `ΔACD`,
`∠ADC+∠CAD+∠ADC=180°`
`⇒40°+∠CAD+80°=180°`
`⇒∠CAD=180°-120°`
`⇒∠CAD=60°`
`"Now" ∠DCT=∠CAD ...........("angles in the alternate segment are equal")`
`∴ ∠DCT=60°`
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