Question

Class 10
Topic - CIRCLES

plz solve the attachment​

Answer 1

Answer:

Given -:

• OP = OR (Radius)
• ANGLE (OPR) = ANGLE (ORP) [ By theorem if opossite sides are equal then angles are also equal ]
• Similarly,OR=OQ (i.e,radius) •HENCE -: ANGLE (ORQ) = ANGLE (OQR)

TO PROOF-:

ANGLE QRS = ANGLE QSR [ BY THIS WE CAN ALSO PROOF THAT QR=QS BY THE THEOREM (opposites angles are equal then opposite sides are also equal)

Step-by-step explanation:

Solution -:

ANGLE OPR = ANGLE ORP [given]

So,

ANGLE ORP = 30°

Now,

ANGLE (OPR + ORP + POR) = 180°

30°+30°+POR = 180 ° { OPR = ORP = 30° }

POR = 180°-60°

POR = 120 ° ✓✓✓

Now, In ∆ORQ

POR + ROQ = 180°

ROQ = 180° - 120° ( POR = 120°)

ROQ = 60°

Similarly we get

RQS = 120°

SO,

RQS + RSQ + QSR= 180°

120° + 30° + QSR = 180°

QSR = 30° ☑️☑️☑️

HENCE QSR = RSQ = 30°

SO BY THEOREM IT WAS ALSO PROVED THAT

QR= QS ✅✅✅✅✅✅✅✅✅✅✅✅