MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Theorem of Equal Chords Subtending Angles at the Center

Seg PM and se...

Question

Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of $∠$ NPM.

Open in App

Solution

Join CN and CM.
In $△$ CPN and $△$ CPM,
PM $≅$ PN (Given)
PC = PC (Common)
CN = CM (Radii)
Thus, $△$ CPN $≅$ $△$ CPM (By SSS congurency)
So, $∠$ CPN = $∠$ CPM (CPCT)
Thus, ray PC is the bisector of $∠$ NPM.

Suggest Corrections

thumbs-up

26

Similar questions

Q. In fig 4.40, seg BC is the diameter of a circle with centre O. if seg AB and seg CD are two chords such that seg AB || seg CD prove that seg AB

≅

Q. In the figure,

s e g

A C

is a diameter of the circle with centre

O .

∠ A B C

intersects the circle at

D .

, s e g

O D ⊥ s e g

A C

Q. In fig. 3.52 consider

□

MNPQ, diagonal MP is perpendicular bisector of diagonal NQ, Then show seg MN

≅

seg MQ, and seg PN

≅

seg PQ. Find the pairs of congruent triangle and justify your answer.

Q. Ray BD is angle bisector of

∠

∆

≅

seg BC, then show that seg. AD

≅

seg DC i.e. seg BD is median of

∆

Q. In the figure, seg

A C

is a diameter of the circle with centre

O

△ A B C

intersects the circle at

D

.
Prove that, seg

O D ⊥ s e g A C

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Circles and Their Chords - Theorem 1

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Theorem of Equal Chords Subtending Angles at the Center

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon