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11. ABC and ADC are two right angled triangles with common hypotenuse AC. Prove that \(\angle{CAD}\) = \(\angle{CBD}\).
Answer :

Draw a circle with AC as diameter passing through B and D. Join BD.
image
\(\triangle{ADC}\) and \(\triangle{ABC}\) are right angled triangles with common hypotenuse.
\(\angle{CBD}\) = \(\angle{CAD}\) ...(Since, angles in the same segment are equal)
Hence, proved.