Question

In the figure, O is the centre of the circle. OE and OF are perpendiculars drawn to the chords AB and CD respectively. If AB = 24cm, CD = 10cm and OE = 5cm, find : a) radius of the circle b) measurment of OF.

Answer 1

Answer:

This question is solely based on the property that perpendicular dropped from the centre of the circle on any chord of that circle will bisect the chord.

Solving (i)

⇒AM=BM=

2

AB

=12cm

Now by applying Pythagorous theorem in △OMB

⇒OB

2

=OM

2

+MB

2

⇒R

2

=5

2

+12

2

=25+144=169[∵OB=Radius]

⇒R=13

Step-by-step explanation:

Solving (ii)

Applying Pythagorous theorem in △OCN

⇒OC

2

=ON

2

+NC

2

[∵OC=Radius=13]

⇒13

2

=12

2

+NC

2

⇒NC

2

=169−144=25

⇒NC=5

Now,since ON is perpendicular to the chord OF

⇒ N is mid point of chord OF

⇒OF=2×NC=2×5=10

Hence, answer of (i) is 13 and that of (ii) is 10