In a triangle ABC, D is the mid point of BC and AD > \\frac{BC}{2}. Then \\angle A is

CAT & OMETs JEE JEE Foundation IPMAT GMAT

Question 2

In a triangle $$ABC$$, $$D$$ is the mid point of $$BC$$ and $$AD > \frac{BC}{2}$$. Then $$\angle A$$ is

Solution

The circle with diameter $$BC$$ has centre $$D$$ and radius $$\frac{BC}{2}$$, and $$\angle A = 90^\circ$$ exactly when $$A$$ lies on it. Since $$AD > \frac{BC}{2}$$, $$A$$ lies outside this circle, so $$\angle A < 90^\circ$$, and hence also $$< 120^\circ$$ and $$< 135^\circ$$. Nothing forces it below $$60^\circ$$ or $$45^\circ$$, so options a, b and c are correct.

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