there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.
OR
Prove that the tangents drawn at the end-points of a chord of a circle make equal angles with the chord.
there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.
OR
Prove that the tangents drawn at the end-points of a chord of a circle make equal angles with the chord.
Answers
Answered by
13
Question;
Prove that the tangents drawn at the end-points of a chord of a circle make equal angles with the chord.
ANSWER;
Given:- A circle with center O,PA and PB are tangents drawn at ends A and B on chord AB.
To prove:- ∠PAB=∠PBA
Construction:- Join OA and OB
Proof:- In △AOB, we have
OA=OB(Radii of the same circle)
∠OAB=∠OBA.....(1)(Angles opposite to equal sides)
∠OAP=∠OBP=90(∵Radius⊥Tangent)
⇒∠OAB+∠PAB=∠OBA+∠PBA
⇒∠OAB+∠PAB=∠OAB+∠PBA(From (1))
⇒∠PAB=∠PBA
Hence proved.
Attachments:
Similar questions
Geography,
2 months ago
Math,
2 months ago
Hindi,
5 months ago
Computer Science,
10 months ago
Math,
10 months ago