In the diagram, A, X, B, C, D are points on the circle. AD is the diameter of the smaller circle. Find the angles AXD and ABC.

April 23, 2026Mathematics

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April 23, 2026

Answer

$90^\circ$

Hapa kuna suluhisho la hatua kwa hatua:

a) Angle AXD Step 1: Identify the type of angle. Angle $AXD$ is an angle subtended by the diameter $AD$ at the circumference of the smaller circle. Step 2: Apply the circle theorem. The angle subtended by a diameter at any point on the circumference is $90^\circ$ . $\angle AXD = 90^\circ$ Reason: Angle in a semicircle. The value of Angle $AXD$ is $\boxed{90^\circ}$ .

b) Angle ABC Step 1: Identify the quadrilateral. $ABCD$ is a cyclic quadrilateral in the bigger circle. Step 2

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Hapa kuna suluhisho la hatua kwa hatua: a) Angle AXD Step 1: Identify the type of angle.

Asked on April 23, 2026Mathematics

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ScanSolve AI AnswerAnswered on April 23, 2026

Hapa kuna suluhisho la hatua kwa hatua: a) Angle AXD Step 1: Identify the type of angle. Angle AXD is an angle subtended by the diameter AD at the circumference of the smaller circle. Step 2: Apply the circle theorem. The angle subtended by a diameter at any point on the circumference is 90^. AXD = 90^ Reason: Angle in a semicircle. The value of Angle AXD is 90^. b) Angle ABC Step 1: Identify the quadrilateral. ABCD is a cyclic quadrilateral in the bigger circle. Step 2