The questions in the image are mathematical problems related to circles. Let me break them down and solve them step by step:

Problem 1 (Soal 1):

Given a circle with radius $r = 2 \, \text{cm}$, determine the following:

a) Find the size of $\angle BDC$:

In this problem, triangle $ABC$ forms a right-angled triangle with $\angle BAP = 90^\circ$. The right-angled triangle and the cyclic properties of the circle help us relate angles.

• The size of $\angle BDC$: The angle $\angle BDC$ will be an inscribed angle that subtends the arc $BC$. For a circle, the inscribed angle that subtends a diameter is $90^\circ$. Since the inscribed angle theorem states that the angle subtended by the diameter is a right angle, $\angle BDC = 90^\circ$.

b) If $\angle CAD = 90^\circ$, determine the size of $\angle ACD$:

• In this case, if $\angle CAD = 90^\circ$, then $\angle ACD$ must be complementary to $\angle ACB$ because the sum of angles in a triangle is $180^\circ$.
• Since $\angle ACB = 90^\circ$, it follows that $\angle ACD = 90^\circ$.

c) Find the length of $CD$:

We are given that the length of $BC = 5 \, \text{cm}$ and the length of the tangent from $B$ to the circle is $8 \, \text{cm}$. In this case, we will use the Pythagorean theorem to find the distance $CD$.

Let me calculate this:

Since $BC$ is the hypotenuse of the right triangle $BCD$, we use the formula: $CD^2 = BC^2 - BD^2$ Given $BC = 5 \, \text{cm}$ and $BD = 8 \, \text{cm}$, we have: $CD = \sqrt{5^2 - 8^2} = \sqrt{25 - 64} = \sqrt{-39}$ This gives an invalid result. We need to clarify the lengths to continue.

Problem 2 (Soal 2):

For the second question about a circle with a radius of 5 cm and a tangent at $BC$ with length $8 \, \text{cm}$, the goal is to determine the apothem. Could you clarify the diagram further or check the given measurements?

Let me know if you'd like further assistance!