CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 20 (For CBSE, ICSE, IAS, NET, NRA 2022)
Get top class preparation for CBSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.
Question 3:
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
Answer:
Given: ABCD is a quadrilateral circumscribing a circle whose center is O.
To prove: (i)
(ii)
Construction: Join OP, OQ, OR and OS.
Proof: Since tangents from an external point to a circle are equal.
In OBP and ,
[Radii of the same circle]
[Common]
[From eq. (i) ]
[By SSS congruence criterion]
Similarly,
Since the sum of all the angles round a point is equal to .
Similarly, we can prove that
Question 4:
In the given 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 .
Answer:
Join
In and , we have
[radius]
Similarly,
Now,
But in ,