मराठी

O is the point of intersection of two chords AB and CD of a circle. If ∠BOC = 80° and OA = OD then ΔODA and ΔOBC are ____________. - Mathematics

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प्रश्न

O is the point of intersection of two chords AB and CD of a circle.

If ∠BOC = 80° and OA = OD then ΔODA and ΔOBC are ____________.

पर्याय

  • equilateral and similar

  • isosceles and similar

  • isosceles but not similar

  • not similar

MCQ
रिकाम्या जागा भरा

उत्तर

If ∠BOC = 80° and OA = OD then ΔODA and ΔOBC are isosceles and similar.

Explanation:

Here, ∠AOD = ∠COB  ...(i) (Vertically opposite angles) 

Also, ∠ODA = ∠OBC  ...(ii) (Angle in the same segment are equal)

Now, In ΔODA and ΔOBC

∠AOD = ∠COB  ...[From (i)]

∠ODA = ∠OBC  ...[From (ii)]

∴ ΔODA ~ ΔOBC  ...(AA similarity)

Since triangles are similar, their sides are proportional

OAOC=ODOB=ADCB

For OAOC=ODOB

Putting OD = OA

OAOC=OAOB

OC = OB

Thus, in ΔOBC,

Two sides are equal, so it is isosceles.

Also in ΔODA,

Given OA = OD, two sides are equal, so it is isosceles

Hence, ΔODA and ΔOBC are isosceles and similar.

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