问题1.画一条长度为8.6cm的线段。将其一分为二并测量每个部分的长度。
解决方案：
Steps of construction:
Step 1: Draw a line segment AB of 8.6cm.
Step 2: With center A and radius more than 1/2 AB, drawn arcs, one on each side of AB.
Step 3: With centre B and same radius, draw arcs cutting the previous arcs at P and Q.
Step 4: Now join in PQ
So, DC = BC = 4.3cm
问题2.画一条长度为5.8cm的线段AB。绘制此线段的垂直平分线。
解决方案：
Steps of construction:
Step 1: Draw a line segment AB of 5.8cm.
Step 2: With centre A radius more than 1/2 AB draw arcs with one on each side of AB.
Step 3: With centre B and same radius draw arcs cutting the previous arcs at P and Q.
Step 4: Now join PQ.
So, PQ is the perpendicular bisector of AB.
问题3.画一个以O点为中心，半径为5cm的圆。绘制其和弦AB，即线段AB的垂直二等分线。它穿过圆心吗?
解决方案：
Steps of construction:
Step 1: With centre O and radius 5cm draw a circle.
Step 2: Now draw a chord AB.
Step 3: With centre A and radius more than 1/2 AB draw arcs one on each side O.
Step 4: With centre B and same radius draw arcs cutting previous arcs at P and Q.
Step 5: Now join point P and Q.
So, the perpendicular bisector PQ of chord AB passes through the center of the circle
问题4.画一个以O点为中心的圆。画出两个和弦AB和CD，使AB不平行于CD。绘制AB和CD的垂直等分线。它们在什么时候相交?
解决方案：
Steps of construction:
Step 1: With centre O and any radiu, draw a circle.
Step 2: Draw two chords AB and CD.
Step 3: With centre A and radius more than 1/2 AB draw arcs, one on each side of AB.
Step 4: With centre B and same radius draw arcs cutting previous arcs at P and Q respective.
Step 5: Join PQ.
Step 6: With centre B and radius more than 1/2 DC draw arcs one on each side of DC.
Step 7: With centre C and same radius, draw arcs cutting previous arcs at R and S.
Step 8: Now join RS.
So, Both perpendicular bisectors PQ and RS intersect each other at the centre O of the circle.
问题5.画一条长度为10cm的线段并将其一分为二。此外，将等分的其中一等分并测量其长度。
解决方案：
Steps of construction:
Step 1: Draw a line segment AB of 10cm.
Step 2: With centre A and radius more than 1/2 AB, draw arcs one on each side of AB.
Step 3: With centre B and same radius draw arcs cutting previous arcs at P and Q respectively.
Step 4: Join PQ and which intersect AB at C.
Step 5: With centre A and radius more than 1/2 AC, draw arcs on each side of AC.
Step 6: With centre C and same radius, radius, draw arcs cutting previous arcs at R and S respectively.
Step 7: Now join RS and which intersect AC at D.
So, AD = 2.5cm
问题6.画一条线AB将其一分为二。将等分之一平分，以获得长度为1/4(AB)的线段。
解决方案：
Steps of construction:
Step 1: Draw a line segment AB.
Step 2:. With cetre A and radius more than 1/2 AB, draw arcs one on each side of AB.
Step 3: With centre B and same radius, draw arcs cutting previous arcs at P and Q.
Step 4: Join PQ which intersects AB at C.
Step 5: With centre A and radius more than 1/2 AC, draw arcs one on each side of AC.
Step 6: Which centre C and same radius, draw arcs cutting previous arcs at R and S.
Step 7: Now join RS Which intersect AC at D.
So, AD = 1/4AB
问题7.画一条线段AB，并用尺子和圆规绘制长度为3/4(AB)的线段。
解决方案：
Steps of construction:
Step 1: Draw a line segment AB.
Step 2: With centre A and radius more than 1/2 AB, draw arcs one on each side of AB.
Step 3: With centre B and same radius draw arcs cutting previous arcs at P and Q.
Step 4: Join PQ which intersect AB at C.
Step 5: With centre C and radius more than 1/2 CB, draw arcs, one on each side of CB.
Step 6: With centre B and same radius draw arcs cutting previous arcs at R and S.
Step 7: Join RS which intersect CB at D.
So, AD = 3/4 AB.
