Class 9 - Mathematics
Circles - Exercise 10.2
Top Block 1
Exercise 10.2
Question :1 : Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
Answer :
Given : Two congruent circles with centres
O and O′. AB and CD are equal chords
of the circles with centres O and O′ respectively.
To Prove: ∠AOB = ∠COD
Proof: In triangles AOB and COD,
AB = CD [Given]
AO = CO’ [Radii of congruent circle]
BO = DO’ [Radii of congruent circle]
∆AOB ≅∆CO′D [by SSS axiom]
Hence, ∠AOB ≅∠CO′D [by CPCT]
Question : 2: Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Answer :
Given : Two congruent circles with
centres O and O′. AB and CD are
chords of circles with centre O
and O′ respectively such that ∠AOB = ∠CO′D
Mddle block 1
To Prove: AB = CD
Proof: In triangles AOB and CO′D,
AO = CO’ [Radii of congruent circle]
BO = DO’ [Radii of congruent circle]
∠AOB = ∠CO′D [Given]
∆AOB ≅∆CO′D [by SAS axiom]
Hence, AB = CD [by CPCT]