ab of △abc and the line through p parallel to bc – Discussion Forum

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Virat

Asked: October 3, 2026In: Class 9 Maths

Suppose P is a point on side AB of △ABC and the line through P parallel to BC meets AC in point Q. For parts (i) to (iii), assume AP = 1, AQ = √5 and see Fig. 12.39. (i) If PB = 2 find QC. (Hint: See the dotted line) (ii) If PB = 1/3 find QC. (Hint: See the dotted lines) (iii) If PB = 2/3 find QC. (Hint: Divide both PB and AP suitably.) (iv) Show that if AP/PB is a rational number, then AP/PB = AQ/QC. In Grade 10, you will prove this equality without assuming AP/PB is rational. That will require a new idea.

(i) QC = 2√5. (ii) QC = √5/3. (iii) QC = 2√5/3. (iv) Dividing AP and PB into equal units and drawing parallels produces congruent intercepts on AC, yielding AP/PB = m/n = AQ/QC. Class 9 maths ganita manjari part 2 ...