O is the centre of circle ABC. AC is produced to D such that CD = CB. If O1 = 128 degrees, prove that D = 32 degrees.

April 18, 2026Mathematics

ScanSolve AI Answer

April 18, 2026

Answer

CB. $\hat{O}_1 = 128^\circ$ .

Here are the solutions to the geometry problems:

Problem (i):

Given: O is the centre of circle ABC. AC is produced to D such that CD = CB. $\hat{O}_1 = 128^\circ$ .
To prove: $\hat{D} = 32^\circ$ .

Step 1: Find the angle at the circumference subtended by arc AB. $\angle ACB = \frac{1}{2} \times \hat{O}_1$ $\angle ACB = \frac{1}{2} \times 128^\circ$ $\angle ACB = 64^\circ$ Reason: Angle at the circumference is half the angle at the centre subtended

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Problem (i): Given: O is the centre of circle ABC. AC is produced to D such that CD = CB.

Asked on April 18, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 18, 2026

Here are the solutions to the geometry problems: Problem (i): Given: O is the centre of circle ABC. AC is produced to D such that CD = CB. O_1 = 128^. To prove: D = 32^. Step 1: Find the angle at the circumference subtended by arc AB. ACB = (1)/(2) × O_1 ACB = (1)/(2) × 128^ ACB = 64^ Reason: Angle at the circumference is half the angle at the centre subtended