ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠ CAD = ∠CBD.
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Answered by
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Given,
AC is the common hypotenuse. ∠B=∠D=90°.
To prove,
∠CAD=∠CBD
Proof:
Since, ∠ABC and ∠ADC are 90°.
These angles are in the semi-circle.
Thus, both the triangles are lying in the semi-circle and AC is the diameter of the circle.
⇒ Points A,B,C and D are concyclic.
Thus, CD is the chord.
⇒∠CAD=∠CBD ...Angles in the same segment of the circle
Answered by
6
Answer:
ANSWER
Given,
AC is the common hypotenuse. ∠B=∠D=90°.
To prove,
∠CAD=∠CBD
Proof:
Since, ∠ABC and ∠ADC are 90°.
These angles are in the semi-circle.
Thus, both the triangles are lying in the semi-circle and AC is the diameter of the circle.
⇒ Points A,B,C and D are concyclic.
Thus, CD is the chord.
⇒∠CAD=∠CBD ...Angles in the same segment of the circle
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