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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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.
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°.
Yes. If ∠AXB = ∠AYB, then A, B, X and Y are concyclic, provided X and Y are on the same side of AB. This follows from Theorem 10.