Gujarat BoardEnglish MediumSTD 9MathsModel Paper 22 Marks
Question
ABC and ADC are two right triangles with common hypotenuse AC. Prove that $\angle CAD =\angle ABD.$
✓
Answer
We have ABC and ADC two right triangles, right angled at B and D respectively. $\Rightarrow \angle ABC=ADC\left[\operatorname{Each} 90^{\circ}\right]$ If we draw a circle with AC (the common hypotenuse) as diameter, this circle will definitely passes through of an arc AC, Because $B$ and $D$ are the points in the alternate segment of an arc $A C$. Now we have $\widehat{ CD }$ subtending $\angle CBD$ and $\angle CAD$ in the same segment. $\therefore \angle CAD=\angle CBD$ Hence proved.
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