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प्रश्न
In the given figure (drawn not to scale) chords AD and BC intersect at P, where AB = 9 cm, PB = 3 cm and PD = 2 cm.
- Prove that ΔAPB ~ ΔCPD.
- Find the length of CD.
- Find area ΔAPB : area ΔCPD.
उत्तर
a. In ΔAPB and ΔCPD,
∠BAP = ∠DCP ...(∠s on same segment)
∠ABP = ∠CDP ...(∠s on same segment)
∴ ΔAPB ~ ΔCPD ...(AA axiom)
b. `(AB)/(CD) = 3/2`
∴ CD = 6 cm
c. `(Area (ΔAPB))/(Area ΔCPD) = (BP^2)/(DP^2)`
= `9/4`
`\implies` 9 : 4
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