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Sum

In Question 5 above, if radii of the two circles are equal, prove that AB = CD.

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#### 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.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

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