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.
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In a cyclic quadrilateral, opposite angles are supplementary. Therefore, ∠C = 180° – 75° = 105°. Similarly, ∠D = 180° – 110° = 70°.
The perpendicular from the centre to the chord bisects the chord. With radius 15 cm and distance 9 cm, half the chord is 12 cm. Therefore, the chord length is 24 cm.
The perpendicular from the centre to the chord bisects the chord. Using the right triangle, half the chord is 12 cm. Therefore, the complete chord is 24 cm.
The quadrilateral ABCD is cyclic. The opposite angles of a cyclic quadrilateral are supplementary. So, x + 100° = 180° Therefore, x = 80°.