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Equal Angles Subtend Equal Sides

Points A,B an...

Question

Points A,B and C are the three vertices of a triangle. The location of point x as such that AX=BX Which of the following can be true?

Only I

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Only III

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Only I and II

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I II and III

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Solution

The correct option is D I II and III
X is on AB
X is inside △ABC
X is outside △ABC All the options are correct.

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Similar questions

D and E are points on the sides AB and AC respectively of a $△$ ABC such that DE || BC. Which of the following statement is true?

(i) $△$ ADE ~ $△$ ABC

(ii) $\frac{a r e a o f △ A D E}{a r e a o f △ A B C}$ = $\frac{A D^{2}}{A B^{2}}$

(iii) $\frac{a r e a o f △ A D E}{a r e a o f △ A B C}$ = $\frac{A B^{2}}{A C^{2}}$

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$△$ ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?

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iii) $D E = \frac{B C}{2}$

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