ICSE Class 9 Answered
PQR is a triangle and PS bisects angle QPR show that (a)PQ>QS (b)PR>RS (c)(PQ+PR)>QR
Asked by sonalagarwalagarwal544 | 03 Jun, 2021, 08:34: AM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/846e73a0a43a074376d833c0fdbc0eb2614844ab623008.23764304f2.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
Since PS bisects
QPR , we have
QPS =
RPS .......................(2)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
From eqn.(1) and (2)
PSQ =
PRS +
QPS
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
Hence
PSQ >
QPS , Hence in Δ PQS , we get PQ > QS ...................(3)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
In similar way , we can get PR > RS ...................... (4)
By adding eqn.(3) and (4) , we get , ( PQ + PR ) > (QS + RS )
we get , ( PQ + PR ) > QS
Answered by Thiyagarajan K | 20 Sep, 2021, 14:04: PM
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