Question

4. If AB, CD are two perpendicular diameters of a circle then AC =​

Answer 1

Answer:

Given:

AB,CD are two perpendicular diameters of a circle

To prove:

AC =AB/√2

PROOF:

1) Let the diameter of the circle is 2R then the radius will be R.

2) The diameter AB and CD are perpendicular to each other so they intersect each other at center let take it O.

3) So ΔAOC will be isosceles right angled triangle where OA and OC are the radius of the circle which is R unit.

4) By the Pythagoras theorem AC = \sqrt{R^{2} +R^{2} }

R

2

+R

2

= R\sqrt{2}R

2

units.

5) Now AB /√2 = 2R/√2 = R\sqrt{2}R

2

units.

Hence AC=AB/√2.

Answer 2

Answer:

AC =AB / √2

Explanation:

AC = AB/ √2

Let the diameter of the circle is 2R then the radius will be R.

2) The diameter AB and CD are perpendicular to each other so they intersect each other at center let take it O.

3) So ΔAOC will be isosceles right angled triangle where OA and OC are the radius of the circle which is R unit.

4) By the Pythagoras theorem AC = = units.

5) Now AB /√2 = 2R/√2 = units.

Hence AC=AB/√2.