NCERT Solutions for Class 9 Maths Chapter 10

Important NCERT Questions

Circles

NCERT Books for Session 2022-2023

CBSE Board, UP Board and Other state Boards

EXERCISE 10.5

Page No:186

Questions No:11

# ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.

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Given: Triangle ABC and ACD are two right triangle on common base AC.

To prove: ∠CAD = ∠CBD.

Proof: Triangle ABC and ADC are on common base BC and ∠BAC = ∠BDC.

Hence, points A, B, C and D lie on the same circle.

[∵ if a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle.]

Therefore,

∠CAD = ∠CBD

[∵ Angles in the some segment are equal]