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प्रश्न
ΔPBC, ΔQBC and ΔRBC are three isosceles triangles on the same base BC. Show that P, Q and R are collinear.
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उत्तर
Given: Three isosceles triangles PBC, QBC and RBC on the same base BC such that PB = PC, QB = QC and RB = RC.
To prove: P, Q, R are collinear.
Proof: Let l be the perpendicular bisector of BC. Since, the locus of points equidistant from B and C is the perpendicular of the segment joining them. Therefore,
ΔPBC is an isosceles
⇒ PB = PC
⇒ P lies on l ...(i)
ΔQBC is isosceles
⇒ QB = QC
⇒ Q lies on l ...(ii)
ΔRBC is an isosceles
⇒ RB = RC
⇒ R lies on l ...(iii)
From (i), (ii) and (iii), it follows that P, Q and R lie on L.
Hence, P, Q and R are collinear.
Hence proved.
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संबंधित प्रश्न
In each of the given figures; PA = PB and QA = QB.
| i. |  |
| ii. |  |
Prove, in each case, that PQ (produce, if required) is perpendicular bisector of AB. Hence, state the locus of the points equidistant from two given fixed points.
Use ruler and compasses only for this question.
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