Q4 of 23 Page 1

Solve sub-questions:

Prove that “the opposite angles of cyclic quadrilateral are supplementary”

Given: □ABCD is a cyclic quadrilateral.

To prove: ∠ BAD+∠BCD = 180°, ∠ABC+∠ADC = 180°



Proof:


⇒ …(I) [inscribed angle theorem]


⇒ …(ii) [Inscribed angle theorem]


Adding equations (I) and (ii), we get


⇒


⇒


⇒ …. [Measures of a circle is 360°]


⇒


In □ABCD,


⇒


⇒


⇒


Hence, the opposite angles of a cyclic Quadrilateral are supplementary.


More from this chapter

All 23 →
3

Solve sub-questions:

Construct the incircle of Δ RST in which RS = 6cm, ST 7 cm, RT


= 6.5 cm.

 3

Solve sub-questions:

Show that:

4

Solve sub-questions:

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river.

4

Solve sub-questions:

A roller of diameter 0.9 m and the length 1.8 m is used to press the ground. Find the area of the ground pressed by it in 500 revolutions.