Solve this: â ‹Q4 In the given figure, ∆ABC circumscribes the circle with centre O - Maths - Circles

Question

Solve this:

â€‹Q4 In the given figure, ∆ ABC
circumscribes the circle with centre O
State whether the following statement is True or False Give reason
also
"If AB + CQ = 8 cm, then the perimeter of â€‹
∆ ABC is 14 cm "

Shruti Tyagi · Accepted Answer

Dear student,

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a0863bfbc4ce%20jpg"
style="width: 195px; height: 141px;">
Let AP=x, BP=z and RC=yGiven: AB+CQ=8 cmClearly, we can see that AB, AC and BC are the tangents to the circle
Then,  AP=AR=x Similarly,RC=QC=yBP=BQ=zNow, Perimeter of ∆ABC=sum of all sides⇒Perimeter of ∆ABC=x+y+z+x+y+z⇒Perimeter of ∆ABC=2x+y+zsince AB+CQ=AP+PB+CQ=x+y+zgiven AB+CQ=8hence 2x+y+z=2×8=16Hence Perimeter of ∆ABC=16 cmTherefore given statement is false
Regards,

Solve this: ​Q4. In the given figure, ∆ ABC circumscribes the circle with centre O. State whether the following statement is True or False. Give reason also. "If AB + CQ = 8 cm, then the perimeter of ​ ∆ ABC is 14 cm."

Solve this:

Q4. In the given figure, $∆$ ABC circumscribes the circle with centre O.
State whether the following statement is True or False. Give reason also.
"If AB + CQ = 8 cm, then the perimeter of $∆$ ABC is 14 cm."