Let NM be a chord of a circle with centre C. Let tangents at M and N meet at the point O. Since OM is a tangent , OM CM, i.e.
OMC = 90 ° Since ON is a tangent , ON CN, i.e.
ONC = 90 ° In D CMN, CM = CN (Radius of the same circle) CMN = CNM. Now, OMC = ONC. OMC – CMN = ONC – CNM. OML = ONL. Thus, tangents make equal angles with the chord .
2/4/2018 · Prove that tangents drawn at the ends of a chord of a circle make equal angles with the chord.
To prove : (i) ?ABC = ?ACB (ii)?XBO = ?OCY. Proof: (i) Using theorem, the length of the tangents drawn form an external point to a circle are equal. ?ABC = ?ACB(? Sides opposite to equal angles are equal) (ii) Using the theorem, the tangent at any point of a circle is perpendicular to the radius through the point of contact. ?XBO = 90°, Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord . asked Jan 12, 2018 in Class X Maths by akansha Expert ( 2.2k points) +3 votes, Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord . Solution Show Solution Let AB be a chord of a circle with centre O, and let AD and BD be the tangents at A and B respectively.
Theorem 10.2 – Class 10 – Tangents from external point of circle are, Ex 10.2, 4 – Prove that tangents drawn at ends of a diameter, Theorem 10.2 – Class 10 – Tangents from external point of circle are, Prove that tangent drawn at the end points of a chord of a circle make equal angles with the chord Get the answers you need, now!, 8/21/2020 · Prove that the tangents drawn at the ends of a chord of circle make equal angles with the chord . Solution: Given: A circle with centre O, PA and PB are tangents drawn at the ends A and B on chord AB. To prove : ?PAB = ?PBA Construction: Join OA and OB. Proof: In ?OAB we have ?? = ?? … (i) [Radii of the same circle] ?2 = ?1.
Answer. Given that: ACB is an arc of the circle with center O, C is the midpoint of arc ACB. Line PQ is the tangent to the circle passing at point C. AB is the chord joining the endpoints A and B of arc. OA =OB …. (Radii of a circle) Draw a perpendicular bisector of chord AB.
5/29/2018 · Ex 10.2,4 Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Given: A circle with center O And diameter AB Let PQ be the tangent at …
5/12/2020 · Transcript. Theorem 10.2 (Method 1) The lengths of tangents drawn from an external point to a circle are equal. Given: Let circle be with centre O and P be a point outside circle PQ and PR are two tangents to circle intersecting at point Q and R respectively To prove : Lengths of tangents are equal i.e. PQ = PR Construction: Join OQ , OR and OP Proof: As PQ is a tangent OQ ? PQ So, ? OQP …
