CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 19
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4 Mark Questions
Question 1:
In figure, XY and X’Y’ are two 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 .

Two Parallel Tangents to a Circle
Answer:
Given: In figure, XY and X’Y’ are two 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.
To Prove:
Construction: Join
Proof:
[Tangent at any point of a circle is to the radius through the point of contact]
In right angled triangles OPA and OCA,
[Common]
[Tangents from an external point to a circle are equal]
[RHS congruence criterion]
[By C.P.C.T.]
………. (iii)
Similarly,
………. (iv)
and a transversal AB intersects them.
[Sum of the consecutive interior angles on the same side of the transversal is ]
………. (v)
[From eq. (iii) & (iv)]
In ,
[Angel sum property of a triangle]
[From eq. (v)]
Question 2:
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact are of lengths 8 cm and 6 cm respectively (see figure). Find the sides AB and AC.

Tangents from an External Point
Answer
Join OE and OF. Also join OA, OB, and OC.

Tangents from an External Point
Since
[Tangents from an external point to a circle are equal]
Since
[Tangents from an external point to a circle are equal]
Let
Since
[Radii of a circle are equal]
Semi-perimeter of
Now, Area of of of
Squaring both sides,
And