Let ABCD be a cyclic quadrilateral having diagonals BD and AC, intersecting each other at point O.
∠BAD=\(\frac{1}{2}\)∠BOD=\(\frac{180^∘}{2}\)=90°
∠BCD+∠BAD=180∘ (Cyclic quadrilateral) (Consider BD as a chord)
∠BCD=180∘−90∘=90°
∠ADC=\(\frac{1}{2}\)∠AOC=\(\frac{1}{2}\)(180)=90
∠ADC + ∠ABC = 180° (Cyclic quadrilateral) °+∠ABC = 180° 90°
∠ADC+∠ABC=180∘ (Opposite angles of a cyclic quadrilateral)
90 °+∠ABC=180∘
ABC = 90° (Considering AC as a chord)
Each interior angle of a cyclic quadrilateral is of 90°. Hence, it is a rectangle.
In Fig. 9.23, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
In Fig. 9.26, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.
In Fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly
(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play