Question

Explain theorem 10.4 in circles class 9

Answer 1

HEY MATE!

THEOREM 10.4:

THE LINE DRAWN THROUGH THE CENTRE IF THE CIRCLE TO BISECT A CHORD IS PERPENDICULAR TO THE CHORD.

GIVEN:

A circle with centre O

AB is a chord of the circle

OX bisects AB

TO PROVE:

OX IS PERPENDICULAR TO AB

PROOF:

IN TRIANGLE OAX AND BOX,

OA =OB(RADIUS)

OX =OX(COMMON)

AX=BX (GIVEN)

HENCE,

TRIANGLE AOX IS CONGRUENT TO TRIANGLE BOX.(SSS RULE)

THEREFORE, ANGLE AOX = ANGLE BXO (CPCT)

IN LINE AB,

ANGLE AXO + ANGLE BXO =180

SINCE, ANGLE AXO = ANGLE BXO

2 ANGLE AXO =180

ANGLE AXO =90

ALSO,

ANGLE BXO =90

HENCE IT IS PROVED. ✨

CHECK OUT THE ATTACHMENT FOR DIAGRAM

Answer 2

Hi there!

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For solutions, Refer to the attached picture.

Regrets for handwriting _/\_

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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.

⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.

⚫ Secant : A line intersecting a circle at any two points, is called secant.

⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.

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