the radius of the circle PB=5cm, diameter AC=10 cm. Find line segment which is part of triangle BPC with an acute right angle.
To find the line segment within triangle BPC that forms an acute right angle, we need to look for a perpendicular bisector of one of the sides.
Step 1: Draw the circle with the given radius.
- Draw a point P as the center of the circle with a radius of 5 cm.
- Sketch a circle around point P with a radius of 5 cm.
- Label the points where the circle intersects as A and C.
Step 2: Draw the diameter.
- Connect points A and C to form diameter AC.
- Label the midpoint of diameter AC as point O.
Step 3: Find the perpendicular bisector.
- Draw a line from point O perpendicular to diameter AC, intersecting the circle at points B and D.
- Label the point of intersection between the line and the circle as B.
- The line segment within triangle BPC, which is BD, will form an acute right angle.
Step 4: Measure the line segment BD.
- To find the length of BD, we need to use the properties of a circle.
- BC is the radius of the circle, which is 5 cm.
Using the Pythagorean theorem, we find the length of BD:
BD^2 + BC^2 = CD^2
Since BC = 5 cm and CD = 5 cm (as they are radii of the circle), we have:
BD^2 + 5^2 = 5^2
Simplifying the equation:
BD^2 + 25 = 25
BD^2 = 25 - 25
BD^2 = 0
Taking the square root of both sides, we find:
BD = √0
Therefore, the length of line segment BD is 0 cm.
Since the length of line segment BD is 0 cm, we conclude that there is no line segment within triangle BPC that forms an acute right angle.