Question

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Answer 1

1answer).

angle CPD=100°

given: AB and CD are congruent chords

angle PAB=40°

angle PAB=angle PBA=40°(angles opposite to angle sides are equal)

angle PAB+angle PBA+angle APB=180°

(angle sum property)

40°+40°+angle APB=180°

angle APB=180°-80°

angle APB=100°

AB=CD

angle CPD=angle APB=100°

(equal angles subtended by equal chords)

therefore, angle CPD=100°

10answer).

angle A=4x

angle C=5x

so, in a cyclic quadrilateral opposite angle=180°

angle A+angle C=180°

4x+5x=180°

x=180°\9

x=20°

angle A=4x=4(20°)=80°

angle C=5x=5(20°)=100°

angle B=5x

angle D=7x

angle B+angle D=180°

5x+7x=180°

12x=180°

x=180°\12

x=15°

angle B=5x=5(12°)=75°

angle D=7x=7(12°)=105°

2answer).

The chord of a circle PQ=?

distance of the chord from the centre OR=4cm

radius of the circle OP=5cm

by using Pythagoras theorem

OP²=OR²+PR²

(5)²=(4)²+PR²

25=16+PR²

PR²=25-16

PR²=9cm

PR=3cm

PR+QR=3+3=6cm(the perpendicular drawn from centre to chord bisects the chord.)

therefore, length of the chord is 6cm

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