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Question -

Equal circles with centre O and O’ touch each other at X. OO’ produced to meet a circle with centre O’, at A. AC is a tangent to the circle whose centre is O. O’ D is perpendicular to AC. Find the value of DO′/CO



Answer -

Two equal circles with centre O and O’ touch each other externally at X
OO’ produced to meet at A
 
AC is the tangent of circle with centre O,
O’D ⊥ AC is drawn OC is joined
AC is tangent and OC is the radius
OC ⊥ AC
O’D ⊥ AC
OC || O’D
Now O’A = 1/2 A x or 1/2 AO
Now in O’AD and AOAC
∠A = ∠A (common)
∠AO’D = ∠AOC (corresponding angles)

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