Q. 535.0( 1 Vote )

# Match the followi

(a) Angle in a semicircle measures – 90° (r)

(b) In the given figure, O is the centre of a circle. If AOB = 120°, then ACB = ?  AOB = ACB

ACB = × 120° = 60°

ACB = 60° (s)

(c) In the given figure, O is the centre of a circle. If and then  Here, OP = OR = OQ (radius)

In ΔPOR

OPR = ORP (angles opposite to equal sides are equal)

By angle sum property

POR + OPR + ORP = 180°

90° + 2×OPR = 180°

OPR = 180°—90°

OPR = 90°

OPR = 45°

Similarly in Δ POQ

OPQ = OQP (angles opposite to equal sides are equal)

By angle sum property

POQ + OPQ + OQP = 180°

110° + 2×OQP = 180°

OQP = 180°–110°

OQP = 70°

OQP = 35°

QPR = QPO + OPR = 45° + 35° = 80°

QPR = 80° (q)

(d) In cyclic quadrilateral it is given that and is a diameter of the circle

through and Then,  Here,

ADC + ABC = 180° (opposite angles in cyclic quadrilateral are supplymentary)

130° + ABC = 180°

ABC = 180°–130° = 50°

In ΔABC

By angle sum property

BAC + ABC + ACB = 180°

BAC + 50° + 90° = 180°

BAC = 180°–50°–90° = 40°

∴∠BAC = 40° (p)

Answers are: (a) – (r), (b) – (s), (c) – (q), (d) – (p)

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