Share
Notifications

View all notifications
Advertisement

In the Given Circle with Center O, ∠Abc=100°, ∠Acd=40° and Ct is Tangent to the Circle at C. Find ∠Adc and ∠Dct. - Mathematics

Login
Create free account


      Forgot password?

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?
Advertisement

APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (C) | Q: 42 | Page no. 288
Advertisement
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.
Advertisement
View in app×