Q. 134.3( 219 Votes )

# D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC. Show that CA^{2} = CB.CD

Answer :

In ΔADC and ΔBAC,

**To Prove : CA**

^{2}= CB . CD**Given: ∠ADC = ∠BAC**

Proof: Now In ΔADC and ΔBAC,

∠ADC = ∠BAC

∠ACD = ∠BCA (Common angle)

According to AA similarity, if two corresponding angles of two triangles are equal then the triangles are similar

ΔADC ΔBAC (By AA similarity)

We know that corresponding sides of similar triangles are in proportion

Hence in ΔADC and ΔBAC,

Hence Proved

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PREVIOUSSides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM ofΔ PQR (see Fig. 6.41). Show thatΔ ABC ~ Δ PQR.
NEXTSides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR.
Show that Δ ABC ~ Δ PQR

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