Having to do with special segments in a circle. P is diameter, BC=5 AD=2 Find PD, ED, PB.
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To find the lengths of segments PD, ED, and PB in a circle with diameter P and given lengths of BC and AD, you will need to use certain properties of circles.
Let's break down the problem step by step:
1. Start by drawing a circle with center O and diameter P. Label points A, B, C, D, and E as shown in the diagram.
A P B
\ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\O/
/ | \
/ | \
/ | \
/ | \
D E C
2. The given lengths are BC = 5 units and AD = 2 units.
3. We know that a diameter of a circle divides it into two equal halves. Thus, segment AD is equal to the radius of the circle, and segment AB is also equal to the radius.
4. Since AD is 2 units, the radius of the circle is 2 units.
5. Now, let's find the lengths of PD, ED, and PB.
To find PD:
- Segment PD is the difference between the diameter (2 * radius) and AD.
- PD = 2 * radius - AD = 2 * 2 - 2 = 4 - 2 = 2 units.
To find ED:
- Segment ED is the sum of the radius and AD.
- ED = radius + AD = 2 + 2 = 4 units.
To find PB:
- Segment PB is equal to the diameter (2 * radius).
- PB = 2 * radius = 2 * 2 = 4 units.
Therefore, the lengths of PD, ED, and PB are as follows:
- PD = 2 units
- ED = 4 units
- PB = 4 units.
Remember, this explanation assumes you have a circle diagram and clear labels for the given points. Visualizing the problem can greatly assist in understanding the concepts and solving for the required lengths.