A foot-bridge is built over a canal in the shape of a semicircular arch

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

A foot-bridge is built over a canal in the shape of a semicircular arch. The ends of the span are points

A

and

B

on the banks, and

AB

60\,\text{m}

long. Two vertical pillars meet the arch at points

P

and

Q

on the same side of the centre such that

AP=18\,\text{m}

and

AQ=24\,\text{m}

. The road surface is along the straight line

AB

. (a) Find the radius of the semicircular arch. (b) Calculate the heights of the pillars

P

and

Q

above the road surface. (c) Determine the difference in the heights of the two pillars.