In the figure (ii) given below, equal circles with centres O and O' touch each other at X. OO' is produced to meet a circle O' at A. AC is tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of (i) (ii)

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KnowledgeBoat · Accepted Answer

From figure, OC is radius and AC is tangent, then OC ⊥ AC. Let radius of each equal circle = r. (i) From figure, AO = AO' + O'X + XO and AO' = O'X = XO = r (radius of circle) AO = r + r + r = 3r. Hence, the value of . (ii) Considering △ADO' and △ACO ∠A = ∠A (Common angles) ∠D = ∠C (Both are equal to 90°) ∴ By AA axiom △ADO' ~ △ACO. Since triangles are similar hence the ratio of their areas is equal to the ratio of the square of the corresponding sides. Hence, the value of

Mathematics

In the figure (ii) given below, equal circles with centres O and O' touch each other at X. OO' is produced to meet a circle O' at A. AC is tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of (i) (ii)

Circles

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