Question

ABCD is a square AB=4 DC is diameter PB tangent find PB

Answer 1

Answer:

PB = 5

Step-by-step explanation:

Let x = PD.

Draw a line PQ parallel to DC with Q on BC, so BPQ is a right angled triangle.

Then:

side PQ of the triangle has length PQ = AB = 4.

side BQ of the triangle has length BQ = BC - CQ = AB - PD = 4 - x.

For side PB, notice that PM and PD are tangents to the circle from P, so PM = PD = x.  Also BM and BC are tangents from B, so BM = BC = 4.  Therefore

side PB of the triangle has length PB = PM + BM = x + 4.

By Pythagoras' Theorem,

( x + 4 )² = 4² + ( 4 - x )²

=> x² + 8x + 16 = 16 + 16 - 8x + x²

=> 16x = 16

=> x = 1

So PB = x + 4 = 5.