Altitude to the hypotenuse of a right triangle: find the altitude or a segment

This type of question, asked 3 times: 17 Sep 2024 S2, 16 Sep 2025 S1, 21 Sep 2025 S3. All 3 questions below, oldest first.

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Question 1
17 Sep 2024 S2
61 $\angle C=90$
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Question 2
16 Sep 2025 S1
71 $A right triangle ABC is inscribed in a circle with a diameter of 10 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. If the length of the leg AB is 6 cm, what is the length of the segment AD?$
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Question 3
21 Sep 2025 S3
75 $A right-angled triangle ABC has legs AB=6 cm and BC=8 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. What is the length of the altitude BD?$
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Question 1