ABCD is a convex quadrilateral that is inscribed in a circle. AB = 10, AD = 24, and m∠BAD = 90°. Find the greatest possible area of ABCD

(1) The length of AB is 6 and the length of CD is 8.

(2) AC is a diameter of the circle.

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Given: Radius = 5

Perimeter of ABCD = AB + BC + CD + AD = ?

St1: The length of AB is 6 and the length of CD is 8. --> AB = 6 and CD = 8

Not Sufficient as value of BC and AD is not known.

St2: AC = diameter = 10 --> ABC and ADC are right angled triangles. Values of the sides of the quadrilateral cannot be derived.

Insufficient

Combining St1 and St2: AB = 6, CD = 8, ABC and ADC are right angled triangles

In ABC, AC = 10, AB = 6 --> BC = sqrt(10^2 - 6^2) = 8

In ADC, AC = 10, CD = 8 --> AD = sqrt(10^2 - 8^2) = 6

Perimeter = AB + BC + CD + AD = 28

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