Question

EXERSICE 10.2 FROM NCERT OF 10TH MATHS CBSE

Q9) IN FIGURE 10.13,XY AND X'Y' ARE 2 PARALLEL TANGENTS TO A CIRCLE WITH CENTER O AND ANOTHER TANGENT AB WITH POINT OF CONTACT c INTERSECTING XY at a AND X'Y'AT B.PROVE THAT

Answer 1

. Given: In figure, XY and X’Y’ are two parallel tangents to a circle with centre O and another
tangent AB with point of contact C intersecting XY at A and X’Y’ at B.
To Prove: AOB =
Construction: Join OC
Proof: OPA = ……….(i)

OCA = ……….(ii)
[Tangent at any point of a circle is to
the radius through the point of contact]
In right angled triangles OPA and OCA,
OA = OA [Common]
AP = AC [Tangents from an external
point to a circle are equal]
OPA OCA
[RHS congruence criterion]
OAP = OAC [By C.P.C.T.]
OAC = PAB ……….(iii)
Similarly, OBQ = OBC
OBC = QBA ……….(iv)
XY X’Y’ and a transversal AB intersects them.
PAB + QBA =
[Sum of the consecutive interior angles on the same side of the transversal is ]
PAB + QBA
= ……….(v)
OAC + OBC =
[From eq. (iii) & (iv)]
In AOB,
OAC + OBC + AOB =
[Angel sum property of a triangle]
+ AOB = [From eq. (v)]
AOB =
Hence proved.

Answer 2

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