In triangle ABC, AB = AC. P is a point on BC such that AP = AB. If angle B = 70°, can such a point P exist strictly between B and C (P not equal to B)?

Question

Accepted Answer

No, only the endpoints B and C work. AB is the shortest of segments from A to BC except the foot, and AP = AB equals the equal side; the only points on BC at distance AB from A are the endpoints B and C, so no strictly interior P exists.

In triangle ABC, AB = AC. P is a point on BC such that AP = AB.
If angle B = 70°, can such a point P exist strictly between B and C (P not equal to B)?

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More Class 9 Properties of Isosceles Triangles practice

In triangle ABC, AB = AC. P is a point on BC such that AP = AB.If angle B = 70°, can such a point P exist strictly between B and C (P not equal to B)?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 Properties of Isosceles Triangles practice

In triangle ABC, AB = AC. P is a point on BC such that AP = AB.
If angle B = 70°, can such a point P exist strictly between B and C (P not equal to B)?