ABCD is a parallelogram. A circle through A, B and C intersects CD (produced) at E. Which of the following is/are <strong>CORRECT</strong>?<br><br>1. AE=AD<br>2. CD=DE<br><br>Select the correct answer using the code given below:

Explanation

Since ABCE is a cyclic quadrilateral, the exterior angle \angle ADE equals interior opposite \angle AEC is incorrect; instead \angle AEC + \angle ABC = 180^\circ. Parallelogram property yields \angle ADC + \angle ABC = 180^\circ. Thus \angle AEC = \angle ADC. Since angles on a straight line give \angle ADE = 180^\circ - \angle ADC, triangle ADE has base angles equal, proving AE=AD.

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