Question

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?

• A. 3.6 cm
• B. 4 cm
• C. 4.8 cm
• D. 6 cm

Answer 1

Answer:

A. 3.6 cm

Since the triangle is inscribed in a circle with diameter (10) cm, the hypotenuse is

$AC = 10\text{ cm}$

Given:

• (AB = 6) cm

• (AC = 10) cm

Using the property of a right triangle,

$AB^2 = AC \cdot AD$

Substitute the values:

$6^2 = 10 \cdot AD$
$36 = 10AD$
$AD = \frac{36}{10} = 3.6\text{ cm}$

Answer:

$\boxed{3.6\text{ cm}}$