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Question
In Question 5 above, if radii of the two circles are equal, prove that AB = CD.
Solution
Join OO’
Since, OA = O’B ...[Given]
Also, ∠OAB = ∠O’BA = 90° ...[Tangent at any point of a circle is perpendicular to the radius at the point of contact]
Since, perpendicular distance between two straight lines at two different points is same.
⇒ AB is parallel to OO’
Similarly, CD is parallel to OO’
⇒ AB ॥ CD
Also, ∠OAB = ∠OCD = ∠O’BA = ∠O’DC = 90°
⇒ ABCD is a rectangle.
Hence, AB = CD.
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