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Question

PX bisects angle P. If True enter 1 else if False enter 0.
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Solution

Given: PQR, QX and RX are bisectors of Q and R and XTPQ and XSQR
Construction: Draw XMPR, Join PX
In XSR and XMR
XRS=XRM (XS bisects R)
XR=XR
XSR=XMR=90
Thus, XSRXMR (ASA rule)
Hence, XS=XM (BY CPCT)...(1)
Similarly, XQSXQT
Hence, XS=XT (By CPCT)....(2)
Hence, by (1) and (2)
XM=XT
Now, In PXT and PXM
XT=XM (Proved above)
XMP=XTP (Each 90)
PX=PX (Common)
Thus, PXTPXM (SAS rule)
Hence, TPX=MPX (by CPCT)
or PX bisects P

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