In a point is chosen inside the triangle such that and

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

In △ABC\triangle ABC a point DD is chosen inside the triangle such that ∠BAD=∠ACD\angle BAD = \angle ACD and ∠ABD=∠ADC\angle ABD = \angle ADC. (i) Prove that △ABD≅△ADC\triangle ABD \cong \triangle ADC. (ii) Deduce that ADAD is perpendicular to BCBC. (iii) If BD=5 cmBD = 5\,\text{cm}, find the length of CDCD.

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