Sure, here is the proof:

Step 1: Let's consider a circle with center O. Let AB be an arc and let's consider two points C and D on the circle such that they subtend ∠COB at the center and ∠DAB at the remaining part of the circle.

Step 2: Draw the radii OC and OD. Also, draw OB.

Step 3: In triangle OCB, ∠COB is an angle subtended by the arc CB at the center.

Step 4: In triangle ADB, ∠DAB is an angle subtended by the same arc CB at the remaining part of the circle.

Step 5: Now, ∠COB = 2 * ∠CAB. This is because the angle subtended by an arc at the center is double the angle subtended by it at any point on the alternate segment of the circle.

Step 6: Therefore, ∠COB = 2 * ∠DAB.

Hence, the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

Question

Sure, here is the proof:

Step 1: Let's consider a circle with center O. Let AB be an arc and let's consider two points C and D on the circle such that they subtend ∠COB at the center and ∠DAB at the remaining part of the circle.

Step 2: Draw the radii OC and OD. Also, draw OB.

Step 3: In triangle OCB, ∠COB is an angle subtended by the arc CB at the center.

Step 4: In triangle ADB, ∠DAB is an angle subtended by the same arc CB at the remaining part of the circle.

Step 5: Now, ∠COB = 2 * ∠CAB. This is because the angle subtended by an arc at the center is double the angle subtended by it at any point on the alternate segment of the circle.

Step 6: Therefore, ∠COB = 2 * ∠DAB.

Hence, the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

Knowee AI · Accepted Answer

Sure, here is the proof:

Step 1: Let's consider a circle with center O. Let AB be an arc and let's consider two points C and D on the circle such that they subtend ∠COB at the center and ∠DAB at the remaining part of the circle.

Step 2: Draw the radii OC and OD. Also, draw OB.

Step 3: In triangle OCB, ∠COB is an angle subtended by the arc CB at the center.

Step 4: In triangle ADB, ∠DAB is an angle subtended by the same arc CB at the remaining part of the circle.

Step 5: Now, ∠COB = 2 * ∠CAB. This is because the angle subtended by an arc at the center is double the angle subtended by it at any point on the alternate segment of the circle.

Step 6: Therefore, ∠COB = 2 * ∠DAB.

Hence, the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

(Prove) The angle subtended by an arc at the center is double the angle subtended by it at anypoint on the remaining part of the circle.

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