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Question
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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Solution
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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| i. |  |
| ii. |  |
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