Draw the perpendicular bisectors of any two sides of the cyclic quadrilateral. Their intersection gives the circumcentre. Then observe whether this point lies inside or outside the quadrilateral.
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Using Brahmagupta’s formula for a cyclic quadrilateral, with sides 5, 5, 12 and 12 units, the semiperimeter is 17 units. Therefore, area = √(12 × 12 × 5 × 5) = 60 square units.
The perpendicular from the centre to the chord bisects it. Half the chord is 8 cm. Using the right triangle, radius² = 8² + 6² = 100. Therefore, radius = 10 cm.
Opposite angles of a cyclic quadrilateral are supplementary. (2x + 10) + (3x – 20) = 180 5x – 10 = 180 x = 38 Thus, ∠P = 86° and ∠R = 94°.
In a cyclic quadrilateral, opposite angles are supplementary. Therefore, ∠C = 180° – 75° = 105°. Similarly, ∠D = 180° – 110° = 70°.