In a circle with center O, chords AB and CD intersect at point E. If CDA = 36^ and CAD = 54^, find COD.

April 24, 2026Mathematics

ScanSolve AI Answer

April 24, 2026

Answer

$\angle OCD = \angle ODC = 36^\circ$

Step 1: Find $\angle COD$ . Since $O$ is the center and $OC = OD$ (radii), $\triangle OCD$ is an isosceles triangle. Given $\angle CDA = 36^\circ$ , which is $\angle ODC$ . Therefore, $\angle OCD = \angle ODC = 36^\circ$ . The sum of angles in $\triangle OCD$ is $180^\circ$ . $\angle COD = 180^\circ - (\angle OCD + \angle ODC) = 180^\circ - (36^\circ + 36^\circ) = 180^\circ - 72^\circ = 108^\circ$

Step 2: Find

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Find COD. Since O is the center and OC = OD (radii), OCD is an isosceles triangle.

Asked on April 24, 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 24, 2026

Step 1: Find COD. Since O is the center and OC = OD (radii), OCD is an isosceles triangle. Given CDA = 36^, which is ODC. Therefore, OCD = ODC = 36^. The sum of angles in OCD is 180^. COD = 180^ - ( OCD + ODC) = 180^ - (36^ + 36^) = 180^ - 72^ = 108^ Step 2: Find