Question

in figure ab is the diameter of the circle and pc is perpendicular to ab. if pc=6cm,pb=3cm,then what is its radius?
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Answer 1

Answer:

Correct option is

A

54.5 cm2

Given:

AB is the diameter =d of a circle.

ΔABC has the diameter AB as base & the point C is on the circumference.

AC=6 cm and BC=8 cm. 

To find out:

Area of shaded portion in the given circle.

Solution:

∠ACB=90o since ΔABC has been inscribed in a semicircle.

∴ΔABC is a right one with AB as hypotenuse    ...(i)

So, applying Pythagoras theorem, we have

AB=(AC)2+(BC)2=(6)2+(8)2 cm=10 cm=d. 

∴ The radius of the given circle =2d=210cm=5 cm. 

i.e The Area of circle =πr2=3.14×52cm2=78.5cm2. 

Again, Area of ΔABC=21×AC×BC (by i)

=21×6×8cm2=24cm2.