Using a ruler and a pair of compass only construct triangle ABC such that |AB|=7cm <|BAC|=45degrees and |AC|=9cm locate a point P inside the triangle ABC which is 5cm from A and equidistant from B and C.find |PB|
using a pair of compasses only. construct triangle ABC in AB=10cm, BC=6cm and Bis 45 degrees . Locate a point D inside the triangle ABC such that D is equidistant from AB and AC and 5cm from B. Construct a straight line through D to cut AB at X and AC at Y such that AX =AY
Step 1: Draw a line segment AB of length 10 cm using a ruler and label the endpoints as A and B.
Step 2: Draw an angle bisector of angle BAC using a compass. Place the compass at point A and draw an arc that intersects AB and AC. Without changing the compass width, place the compass at point B and draw an arc that intersects the previously drawn arc. Label the point of intersection as C.
Step 3: Draw a perpendicular bisector of AB using a compass. Place the compass at point A and draw an arc that intersects AB. Without changing the compass width, place the compass at point B and draw an arc that intersects the previously drawn arc. Label the point of intersection as E.
Step 4: Draw a circle with center D and radius 5 cm using a compass. Place the compass at point B and draw an arc that intersects the previously drawn circle. Label the points of intersection as F and G. Note that point D is the midpoint of line segment FG since it is equidistant from points B and C.
Step 5: Draw a line through point D that intersects line segment AB at point X and line segment AC at point Y such that AX = AY using a compass. Place the compass at point D and draw an arc that intersects line segment AB and line segment AC. Label the points of intersection as X and Y, respectively.