In given figure, if `angleA=angleC`, AB= 6 cm, BP = 15 cm, AP = 12 cm and CP= 4 cm, then find the lengths of PD and CD.

Explanation

Given, `angleA=angleC`, AB= 6cm ,BP= 15 cm, AP= 12 cm and CP = 4 cm
In `DeltaAPB and DeltaCPD`, `angleA=angleC` [given]
`angleAPB=angleCPD` [vertically opposite angles]
`therefore DeltaAPD~DeltaCPD` [by AAA similarity criterion]
`rArr (AP)/(CP)=(PB)/(PD)=(AB)/(CD)`
`rArr 12/4=15/(PD)=6/(CD)`
On taking first two terms, we get
`12/4=15(PD)`
`rArr PD=(15xx4)/12=5 cm`
On taking first and last term, we get
`12/4=6/(CD)`
`rArrCD=(6xx4)/12=2 cm`
Hence, length of PD= 5 cm and length of CD = 2cm