please solve it

Asked by gpnkumar0 | 25th Feb, 2018, 10:06: PM

Expert Answer:

begin mathsize 16px style According space to space the space question space increment ABC space is space right space triangle space in space which space angle ABC equals 90 degree
straight A space circle space is space drawn space on space side space AB space as space diameter space intersecting space AC space at space straight P.
PQ space is space tangent space to space the space circle space when space intersect space BC space at space straight Q.
Join space BP

PQ equals BQ space space space space space space space space space space space space Tangent space from space external space point
angle PBQ equals angle BPQ space space Opposite space angles space of space equal space sides
AB space is space diameter space of space the space circle.
angle APB equals 90 degree.............. left parenthesis straight i right parenthesis angle space in space semi minus circle
angle APB plus angle BPC equals 180 degree space space space space Linear space pair
From space left parenthesis straight i right parenthesis space
angle BPC equals 90 degree........... left parenthesis ii right parenthesis space space
In space increment BPC
angle BPC plus angle PBC plus angle PCB equals 180 degree space space space space space Angle space sum space property
From space left parenthesis ii right parenthesis
angle PBC plus angle PCB equals 90 degree...... left parenthesis iii right parenthesis
Now comma
angle BPQ plus angle CPQ equals 90 degree.......... left parenthesis iv right parenthesis
From space left parenthesis iii right parenthesis space and space left parenthesis iv right parenthesis
angle PBC plus angle PCB equals angle BPQ plus angle CPQ
angle PCQ equals angle CPQ space space space space space space space space space space space space space space space space space space space space space space space angle PCQ equals angle PBQ
In space increment PQC
angle PCQ equals angle CPQ space space space space space space space
PQ equals QC..... left parenthesis straight v right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis straight v right parenthesis
BQ equals QC
Tangent space at space straight P space bisects space side space BC.

end style

Answered by Sneha shidid | 26th Feb, 2018, 11:12: AM