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प्रश्न
Given: ∠BAC, a line intersects the arms of ∠BAC in P and Q. How will you locate a point on line segment PQ, which is equidistant from AB and AC? Does such a point always exist?
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उत्तर
Since, locus of points equidistant from AB and AC is the bisector of ∠BAC. Draw the bisector of ∠BAC intersecting PQ at R.
Since,R is on the bisector, so it is equidistant from AB and AC.
Yes, such a point always exists as there will be definitely a point where angular bisector and line will intersect.
Hence, R is the required point.
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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.
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- P is equidistant from B and C.
- P is equidistant from AB and BC.
- Measure and record the length of PB.
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