In which of the following triangles does the orthocentre lie in the exterior of the triangle?

(a)

Δ A B C, w h e r e i n, ∠ A = ∠ B = ∠ C = 60^{\circ}

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(b)

Δ P Q R, w h e r e i n, ∠ P = 40^{\circ}, ∠ Q = 30^{\circ}, ∠ R = 110^{\circ}

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(c)

Δ X Y Z, w h e r e i n, ∠ X = 80^{\circ}, ∠ Y = 60^{\circ}, ∠ Z = 40^{\circ}

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(d)

Δ D E F, w h e r e i n, ∠ D = 52^{\circ}, ∠ E = 90^{\circ}, ∠ F = 38^{\circ}

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Solution

The correct option is B (b) $Δ P Q R, w h e r e i n, ∠ P = 40^{\circ}, ∠ Q = 30^{\circ}, ∠ R = 110^{\circ}$

with angle $110 °$ ,
orthocenter does lie exterior of triangle.
Hence, $△$ PQR wherein, $∠$ P= $40 °$ , $∠$ Q= $30 °$ , $∠$ R= $110 °$ .

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Question 29

In $Δ P Q R$ , if $∠ P = 60^{\circ}$ and $∠ Q = 40^{\circ}$ , then the exterior angle formed by producing QR is equal to

a) $60^{\circ}$
b) $120^{\circ}$
c) $100^{\circ}$
d) $80^{\circ}$

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In which of the following triangles does the orthocentre lie in the exterior of the triangle?

The correct option is B (b)ΔPQR,wherein,∠P=40∘,∠Q=30∘,∠R=110∘with angle 110° , orthocenter does lie exterior of triangle.Hence, △PQR wherein, ∠P=40°, ∠Q=30°,∠R=110°.

The correct option is B (b) $Δ P Q R, w h e r e i n, ∠ P = 40^{\circ}, ∠ Q = 30^{\circ}, ∠ R = 110^{\circ}$

with angle $110 °$ ,
orthocenter does lie exterior of triangle.
Hence, $△$ PQR wherein, $∠$ P= $40 °$ , $∠$ Q= $30 °$ , $∠$ R= $110 °$ .