In the given figure, AT is a tangent to the circle at B. If angle ABT = 80 degrees and chord BC = chord CD, find angle BDC (x).

Here are the solutions for the geometry problems: d) Step 1: Identify the given information. We are given that line AT is tangent to the circle at B. Angle ABT = 80°. Chord BC = Chord CD (indicated by the double dashes). We need to find the value of x, which is ∠ BDC. Step 2: Apply the Alternate Segment Theorem. The angle between the tangent AT and the chord BD is ∠ ABT. This angle is equal to the angle subtended by the chord BD in the alternate segment, which is ∠ BCD. So, ∠ BCD = ∠ ABT = 80°.

In the given figure, AT is a tangent to the circle at B. If angle ABT = 80 degrees and chord BC = chord CD, find angle BDC (x).

Here are the solutions for the geometry problems: d) Step 1: Identify the given information. We are given that line AT is tangent to the circle at B. Angle ABT = 80°. Chord BC = Chord CD (indicated by the double dashes). We need to find the value of x, which is ∠ BDC. Step 2: Apply the Alternate Segment Theorem. The angle between the tangent AT and the chord BD is ∠ ABT. This angle is equal to the angle subtended by the chord BD in the alternate segment, which is ∠ BCD. So, ∠ BCD = ∠ ABT = 80°.

Solved: In the given figure, AT is a tangent to the circle…

Here are the solutions for the geometry problems:

Identify the given information.
We are given that line AT is tangent to the circle at B.
Angle ABT = 80°.
Chord BC = Chord CD (indicated by the double dashes).
We need to find the value of x, which is $\angle BDC$ .
Apply the Alternate Segment Theorem.
The angle between the tangent AT and the chord BD is $\angle ABT$ . This angle is equal to the angle subtended by the chord BD in the alternate segment, which is $\angle BCD$ .
So, $\angle BCD = \angle ABT = 80^\circ$ .

In the given figure, AT is a tangent to the circle at B. If angle ABT = 80 degrees and chord BC = chord CD, find angle BDC (x).

Step-by-step solution

Identify the given information.

Apply the Alternate Segment Theorem.

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