Mathematics
D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. Show that CA2 = CB.CD.
Triangles
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Answer
Δ ABC is shown in the figure below:
In Δ ABC and Δ DAC,
⇒ ∠BAC = ∠ADC (Given)
⇒ ∠ACB = ∠ACD (Common angles)
∴ Δ ABC ∼ Δ DAC (By A.A. axiom)
We know that,
Corresponding sides of similar triangle are proportional.
⇒ CA2 = CB × CD.
Hence, proved that CA2 = CB × CD.
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