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Question
Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = `3/4` AB and AQ = `1/4` AC. Join P and Q and measure the length PQ.
Solution
Steps of construction:
- Draw a line segment AB = 5 cm.
- Draw ∠BAZ = 60°.
- With centre A and radius 7 cm, draw an arc cutting the line AZ at C.
- Draw a ray AX, making an acute ∠BAX.
- Divide AX into four equal parts, namely AA1 = A1A2 = A2A3 = A3A4.
- Join A4B.
- Draw A3P || A4B meeting AB at P.
- Hence, we obtain, P is the point on AB such that AP = `3/4` AB.
- Next, draw a ray AY, such that it makes an acute ∠CAY.
- Divide AY into four parts, namely AB1 = B1B2 = B2B3 = B3B4.
- Join B4C.
- Draw B1Q || B4C meeting AC at Q. We get, Q is the point on AC such that AQ = `1/4` AC.
- Join PQ and measure it.
- PQ = 3.25 cm.
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