#### 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°`

Is there an error in this question or solution?

Solution In the Given Circle with Center O, ∠Abc=100°, ∠Acd=40° and Ct is Tangent to the Circle at C. Find ∠Adc and ∠Dct. Concept: Number of Tangents from a Point on a Circle.