Request a call back

Two circles touch each other externally at C and AB is a common tangent to the circles. Then, ACB=
Asked by | 05 Jan, 2013, 08:56: PM

Let A be on a circle with centre O and B be the point on the circle with O' as centre. And AB be the tangent to both circles touching at A and B.

Let the two circles touch at C.

Let the tangent at C meet AB at N.

Now, NA and NT are tangents to the the circle with centre O andtherefore NA= NB. So the triangle NAC is isosceles and angles NAC = NCA = x say.

By similar consideration NB and NT are tangents from N to circle with centre O'. So triangle NBC is isosceles with NB=NC and therefore, angles NBC = NCB = y say.

Therefore in triangle ABC, angles A+B+C = x + y + (x+y) = 180

Or 2(x+y) =180.

x+y = 180/2 = 90.

Therefore,

x+y = angle ACB =180/2 =90 degree.

Answered by | 06 Jan, 2013, 01:19: PM
CBSE 10 - Maths
Asked by sheetal.kolte | 15 Mar, 2024, 03:25: PM
CBSE 10 - Maths
Asked by rajk7371198 | 09 Feb, 2024, 11:55: PM
CBSE 10 - Maths
Asked by mp2235793 | 11 Jan, 2024, 10:31: PM
CBSE 10 - Maths
Asked by lakshmimanjula433 | 19 Nov, 2023, 10:50: AM
CBSE 10 - Maths
CBSE 10 - Maths